
537 F.3d 439 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Ignacio RAMOS; Jose Alonso Compean, Defendants-Appellants.
No. 06-51489.
United States Court of Appeals, Fifth Circuit.
July 28, 2008.
*442 Joseph H. Gay, Jr., Mark Randolph Stelmach (argued), Asst. U.S. Attys., San Antonio, TX, for U.S.
David L. Botsford (argued), Law Office of David L. Botsford, Austin, TX, Mary Stillinger, El Paso, TX, for Ramos.
J. Mark Brewer, Brewer & Pritchard, Houston, TX, Richard Abbott Samp, Daniel J. Popeo, Paul D. Kamenar, Washington, Legal Found., Washington, DC, for Amici Curiae.
Before JOLLY, HIGGINBOTHAM and PRADO, Circuit Judges.
E. GRADY JOLLY, Circuit Judge:
The two Border Patrol agents, appellants Ignacio Ramos and Jose Compean, were engaged in routine law enforcement along the United States-Mexico border near Fabens, Texas, when they became involved in chasing an alien drug smuggler driving a van as he speeded toward the Mexican border. After the drug smuggler abandoned the van and began to run on foot toward the Mexican border, the agents gave chase, fired their weapons at him several times, and hit him once, but the wound did not prevent his escape into Mexico.
After the incident, there was a "cover-up"  including a clean-up of the area of spent shells and a failure by the two agents to report the weapon-firing incident, as plainly required by well-established Border Patrol policies.
But through a series of fortuitous events, the incident was revealed and then investigated by the Border Patrol. That investigation resulted in these convictions of the two agent-appellants for numerous offenses relating to unlawfully discharging their weapons and concealing the offense. They are now serving lengthy terms in prison.
At trial, the facts were sharply and hotly disputed. The government's evidence showed that the agents had no reason to shoot the drug smuggler  that he had abandoned his van loaded with marijuana, that he was running on foot back to Mexico, that he posed no physical threat to either officer, and that he was shot in the buttocks. It is well established that the Fourth Amendment to the United States Constitution does not permit officers to shoot a fleeing suspect unless the suspect poses a threat to the physical safety of the officers or to the public.
The defendants' evidence presented a much different version of the facts from that presented by the government. They testified that they saw something appearing to be a weapon in the drug-smuggler's hand, that the situation was tense, that they felt in danger, that they acted as reasonable officers in pursuit of a possibly dangerous drug smuggler, and that firing a weapon was justified. Furthermore, they testified that their failure to report the incident was only a matter of negligence.
Once at trial, this case was hardly more than a dispute between these two sets of facts.
The jury was the fact-finder. The jury heard all of the evidence. The jury returned *443 the verdict. The jury did not believe the Border Patrol agents. It convicted them. The government's evidence, if believed, is sufficient to uphold the convictions. And that is pretty close to the bottom line on guilt or innocence of these agents.
On appeal, we will address some of the errors, legal and evidentiary, alleged to have been committed by the trial court. Many arguments are made by the agents. We will address their primary arguments and we will find merit in some. Accordingly, we will reverse and vacate the convictions on some counts and vacate the sentences on those counts. However, this may not be of much moment to Ramos and Compean because we leave the major conviction with the major sentence  18 U.S.C. § 924(c)  untouched.
In this prefatory statement we should note that the rather lengthy sentences imposed on the defendants  eleven years and a day and twelve years respectively  result primarily from their convictions under § 924(c). Why? Because Congress directed a mandatory minimum sentence of ten years for all defendants convicted under this statute, i.e., using a gun in relation to the commission of a crime of violence. The underlying crime of violence with which the defendants were charged is assault within the special territorial jurisdiction of the United States. Once the defendants were charged by the government and convicted by the jury under this statute, the district court had no discretion but to impose at least a ten-year sentence. Thus, the sentences in this case reflect the mandatory ten years for violation of § 924(c), and one year and a day and two years, respectively, for the remaining several convictions.
The defendants were convicted for assault, discharge of a weapon in the commission of a crime of violence, tampering with an official proceeding, and deprivation of civil rights. We AFFIRM all convictions except those for tampering with an official proceeding, which we VACATE. We REMAND for resentencing.
We turn now to consider the appeal and begin with a more comprehensive rendition of the facts.

I.
As we have indicated, this case features competing narratives. The government argues that the defendants acted effectively as vigilantes, shooting Oswaldo Aldrete-Davila without adequate provocation and then attempting to cover up their crime by failing to report the shooting and, in the case of Compean, by destroying evidence. The defendants vigorously press a different version of events, one in which they responded to a direct threat posed by Aldrete-Davila and subsequently made innocent mistakes related to their reporting duties.
The investigation that led to the defendants' arrests, trial, and convictions began on February 28, 2005, with Rene Sanchez, a Border Patrol Agent stationed in Arizona. Sanchez learned from his mother-in-law that a long-time personal acquaintance of his, Aldrete-Davila, had been shot while attempting to escape the Border Patrol in Texas. Agent Sanchez contacted Aldrete-Davila, who confirmed that he had been shot by the Border Patrol earlier that month, on February 17. Agent Sanchez reported what he had learned to his supervisor, who instructed him to continue investigating the incident. But Agent Sanchez was frustrated in this attempt. He consulted the Border Patrol's national database of reported firearms discharges, but found no record corresponding to Aldrete-Davila's report. Agent Sanchez spoke with Aldrete-Davila again in March *444 2005 and learned that the bullet from the shooting was still lodged in Aldrete-Davila's body. Agent Sanchez included this information in the memorandum of the investigation that he filed.
The investigation into the border shooting was then taken up by Christopher Sanchez, a special agent with the Office of the Inspector General in the Department of Homeland Security. Like Rene Sanchez, Special Agent Sanchez was unable to find any record of a reported shooting on February 17, 2005. But he did determine that the shooting had happened near Fabens, Texas. He located the specific area in which the shooting was reported to have happened, but found no evidence  shell casings or otherwise  that would have identified the Border Patrol agents involved in the shooting.
Special Agent Sanchez made contact with Aldrete-Davila, but found that Aldrete-Davila was unwilling to speak to him due to concerns about prosecution in the United States. Ultimately, Aldrete-Davila's fears were allayed with a promise of immunity from the United States Attorney. Special Agent Sanchez delivered the immunity agreement to Aldrete-Davila in Mexico and explained to Aldrete-Davila that, in exchange for his truthful testimony, the government would not prosecute him for the February 17 events. Aldrete-Davila agreed to cooperate. Still, Special Agent Sanchez was unable to ascertain the identity of the Border Patrol agents involved in the shooting. Aldrete-Davila was then brought to the United States so that the bullet could be removed from his body for use in Special Agent Sanchez's investigation.
Special Agent Sanchez then obtained the firearms of all the Fabens area Border Patrol agents on duty on the day of the shooting. The bullet was matched with the firearm of Ignacio Ramos. Based on this evidence and the testimony of another Border Patrol agent, Special Agent Sanchez was ultimately able to identify Ramos and Compean as the Border Patrol agents who had fired upon Aldrete-Davila.
Aldrete-Davila is a drug trafficker. On the day he was shot, he had agreed to transport drugs already located in the United States. He illegally crossed the border on February 17 in order to reach a van that he had agreed to drive. The van was parked near Fabens and contained a large load of marijuana. The keys to the van were already in its ignition, and Aldrete-Davila began driving it towards Fabens.
Compean was patrolling the area near where Aldrete-Davila crossed the border and was alerted to a border crossing by a surveillance sensor. Compean reported a van leaving the area over his radio. Border Patrol Agent Oscar Juarez then spotted the van. At this point, Aldrete-Davila decided to try to escape back into Mexico, and a high-speed pursuit began. Agent Juarez was eventually joined by Ramos, who took the leading position in the chase. During this period, the pursuing agents communicated directly with one another; the Border Patrol station did not receive or record their communications, leaving their supervisors generally unaware of the details surrounding the pursuit.
The chase ended when Aldrete-Davila's van became stuck at the edge of a deep irrigation ditch near the Rio Grande river. Aldrete-Davila left the van and went into the ditch, intending to cross it, flee across the vega behind it, and reach the Rio Grande. Aldrete-Davila made it to the other side of the ditch and found Compean waiting for him on the levee road bordering the ditch. At this point, stories presented to the jury begin to diverge. Compean was holding his shotgun and testified that he told Aldrete-Davila to stop and put *445 his hands up, an order that Compean testified Aldrete-Davila failed to obey. Compean testified that he tried to push Aldrete-Davila back with his shotgun, but slipped. According to Compean, Aldrete-Davila then ran towards the Mexican border and Compean threw down his shotgun and began pursuit. Compean testified that he pursued and caught up with Aldrete-Davila, tackled him, but ultimately was unable to prevent Aldrete-Davila from escaping his grasp. Aldrete-Davila presented a different version of these events.
Agent Juarez testified that, after arriving at the scene, he saw Aldrete-Davila get out of the van and move quickly into the ditch and up the other side. Contrary to Compean's account, Agent Juarez testified that Aldrete-Davila's hands were raised and that Compean attempted to take a full swing at Aldrete-Davila with the stock of the shotgun. According to Agent Juarez, Compean missed, fell to the ground, and dropped his shotgun into the ditch. Agent Juarez testified that he saw Compean begin to pursue Aldrete-Davila and, thinking there was no danger, turned towards the van to begin an investigation of its contents. He testified that he then heard shots and saw Compean firing his handgun toward the border, although, apparently because of the slope of the land, he did not see Compean's target. Agent Juarez further testified that he saw Compean change the magazine of his weapon and fire again.
Compean testified that he was on the ground because Aldrete-Davila had thrown dirt into his face, but that he saw Aldrete-Davila run a short distance and then turn with something in his hand, putting Compean in fear for his life. Compean testified that he rose to one knee and began firing his weapon, but lost sight of Aldrete-Davila when he attempted to do a magazine exchange. Compean testified that he heard an additional shot, and then saw Ramos.
Ramos testified that, after he had stopped his car behind Aldrete-Davila's van, he saw Aldrete-Davila evade Compean at the ditch, but saw no confrontation of the type described by the other witnesses. Ramos testified that after he entered the ditch, he heard firing. Upon reaching the levee road, Ramos testified that Compean was on the ground and that he saw Aldrete-Davila with something in his hand. Ramos testified that he then fired a single shot.
Aldrete-Davila denied turning around and denied having any object in his hand. He instead insisted that he simply ran towards the border, saw dirt being kicked up around him by bullets, and then fell, feeling a burning sensation in his left buttock. He testified that he waited for Ramos and Compean to arrest him, but saw them turn away. Aldrete-Davila eventually made it back over the border. He was apparently met by the drug traffickers for whom he was working and was taken to a medical facility. The bullet fired by Ramos had fragmented, severing Aldrete-Davila's urethra. But the wound offered no conclusive corroboration of any witness's version of events.
Ramos and Compean returned to the ditch. On the way, Compean picked up some of his ejected shell casings and threw them into the water in the irrigation ditch. A later-arriving Border Patrol agent, Arturo Vasquez, testified that he was approached by Compean and was asked by Compean to find the spent shell casings that Compean had not been able to recover. After making sure that he was alone, Agent Vasquez found four spent casings and threw them into the water in the irrigation ditch.
At the scene, Compean was asked by a supervisor if he had been assaulted and *446 responded that he had not been. Neither he, nor Ramos, nor several of the other agents who had heard shots reported to their supervisors that a weapons discharge had taken place. All agree that this failure to report was a violation of clearly-established Border Patrol policy. Nor did the defendants report that they had been threatened by Aldrete-Davila. Ramos and Compean suggested that their failures in reporting that they fired their weapons arose variously from simple mistake and fear of getting in trouble. After they were identified as the shooters by Special Agent Sanchez, they were arrested and charged with a number of crimes related to firing upon Aldrete-Davila and failing to report the shooting.

II.
The indictment charging Ramos and Compean enumerated twelve counts.[1] These counts included charges for attempted murder, criminal assault, unlawful discharge of firearms, tampering with official proceedings, and criminal deprivation of civil rights. After a lengthy trial, Ramos and Compean were found guilty on all charges save attempted murder, for which they were acquitted. Under the Federal Sentencing Guidelines, both defendants were eligible for roughly fifteen years of imprisonment. In this connection, we say again that the sentence is predominantly influenced by their convictions under 18 U.S.C. § 924(c)(1)(A), which carried mandatory minimum terms of ten years. Ramos was ultimately sentenced to eleven years and Compean to twelve years. They now appeal, alleging numerous errors at trial.

III.
Ramos raises fourteen points of error and Compean raises twelve. There is some overlap in the issues that they raise, and some have minimum merit that only requires limited consideration here. The defendants first contend that they were improperly precluded from introducing relevant evidence  specifically evidence concerning other drug-trafficking activities in which Aldrete-Davila was allegedly involved, occurring after the incident here. The defendants urge that barring them from presenting this evidence denied them their Sixth Amendment right to a complete defense.
The defendants also challenge their convictions under the firearm statute, 18 U.S.C. § 924(c)(1)(A)  the convictions that carry a mandatory minimum sentence and which resulted in the bulk of their total prison sentences. They raise both Due *447 Process and Equal Protection challenges to their convictions, while also claiming that the indictment was flawed in charging them with this crime.
The government produced evidence showing that the defendants violated a number of Border Patrol policies in pursuing and firing upon Aldrete-Davila. The defendants characterize the trial as one in which the Border Patrol policies were substituted for the actual crimes charged and that by permitting evidence that established policies were violated and strict rules were broken the district court allowed the government to avoid the more difficult task of showing that the defendants had engaged in criminal conduct.
The defendants were charged with tampering with an official proceeding under 18 U.S.C. § 1512(c) by failing to report the shooting to their supervisors. They argue on a number of grounds that such a failure to act constitutes neither tampering with evidence nor inhibiting an official proceeding, an argument that we conclude has merit.
Finally, they repeatedly challenge the jury's verdict that rejected their version of the events: They argue that, as law enforcement officers, they were justified in shooting Aldrete-Davila because of the threat that they thought he posed to them. They argue that they are entitled to this justification defense even if they were reasonably mistaken in their perception of that threat. The defendants argue that their rights in this respect were not adequately included in the jury instructions. The defendants' theory that they were justified in shooting Aldrete-Davila also animates their last argument. The defendants contend that there was not sufficient evidence to convict them for the substantive criminal offenses related to discharging their firearms precisely because they were acting in accord with their duties of law enforcement. We now turn to address the arguments presented.

IV.

A.
The defendants first raise Sixth Amendment issues. They argue that they were improperly limited in presenting evidence at trial and in cross-examining Aldrete-Davila, who testified as a witness for the government. To the point, the defendants argue that they should have been allowed to introduce evidence of the value and amount of drugs transported by Aldrete-Davila; further, they argue that they were improperly limited in cross-examining Aldrete-Davila  and in producing evidence  regarding his alleged involvement in another drug-trafficking incident that occurred in October 2005, that is, after the events that are the subject of this trial. The limitations imposed by the district court, the defendants contend, violated their Sixth Amendment[2] rights to confront a witness called against them and, secondly, their right to present a complete defense.

1.
These respective Sixth Amendment rights claimed by the defendants are closely related. See Kittelson v. Dretke, 426 F.3d 306, 318 (5th Cir.2005) ("The Sixth Amendment right to present a complete *448 defense encompasses a defendant's rights under the Confrontation Clause to rebut the State's evidence through cross-examination."). The right to present a complete defense under the Sixth Amendment "is an essential attribute of the adversary system. However, this right is limited and must be weighed against the countervailing interests in the integrity of the adversary process ... the interest in the fair and efficient administration of justice, and the potential prejudice to the truth-determining function of the trial process." United States v. Mizell, 88 F.3d 288, 294 (5th Cir.1996) (alteration in original, internal quotation marks and citations omitted). A trial court's restrictions in this respect are reviewed for harmless error. See id. at 295.
Similar principles apply to the rights guaranteed to criminal defendants under the Sixth Amendment's Confrontation Clause:
The Supreme Court has recognized that trial judges retain wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on cross-examinations based on among other things, harassment, prejudice, confusion of the issues, the witness' safety, or interrogation that is repetitive or only marginally relevant. The relevant inquiry is whether the jury had sufficient information to appraise the bias and motives of the witness.
United States v. Tansley, 986 F.2d 880, 886 (5th Cir.1993) (internal citation omitted). "A district court's limitation of cross-examination of a witness is reviewed for abuse of discretion. Abuse-of-discretion review is only invoked if the limitation did not curtail the defendant's Sixth Amendment right to confront witnesses. Whether a defendant's Sixth Amendment rights were violated is reviewed de novo." United States v. Hitt, 473 F.3d 146, 155-56 (5th Cir.2006) (internal citation omitted). Thus, the rights guaranteed by the Sixth Amendment are substantial but are not independent of the trial court's duty to ensure a fair trial. See Taylor v. Illinois, 484 U.S. 400, 410-13, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988).
In connection with the defendants' assertion of their Sixth Amendment rights, Aldrete-Davila invoked his Fifth Amendment privilege against self-incrimination on cross-examination and refused to answer certain questions posed to him by the defendants. When these two constitutional rights intersect, "[a] valid assertion of the witness' Fifth Amendment rights justifies a refusal to testify despite the defendant's Sixth Amendment rights." United States v. Goodwin, 625 F.2d 693, 700 (5th Cir.1980). Further, the district court has broad discretion in evaluating a witness's claim of privilege under the Fifth Amendment. See United States v. Hernandez, 962 F.2d 1152, 1161 (5th Cir.1992).
At the outset of our analysis, we further note that the Sixth Amendment issue tends to get overshadowed, at times, by the subsidiary questions relating to the nature of the immunity agreement between Aldrete-Davila and the U.S. Attorney. Nevertheless, the immunity agreement is at issue only because of the Sixth Amendment rights raised by the appellants. They contend that during their cross-examination the district court improperly allowed Aldrete-Davila to assert his Fifth Amendment right not to answer certain questions concerning a subsequent drug-trafficking incident notwithstanding his immunity agreement.

2.
We first consider the argument that the defendants were restricted from presenting evidence detailing the amount and value of the marijuana in the van driven by *449 Aldrete-Davila. The defendants argue that, because they could not present the details of the marijuana load, they were prevented from effectively presenting arguments related to Aldrete-Davila's motives to flee, to protect his investment, and to avoid prosecution for his crime, which, in turn, they argue is relevant to the central issue of whether Aldrete-Davila likely would have possessed and brandished a gun, thereby justifying the defendants firing their weapons and wounding him.
At trial, evidence  both testimonial and photographic  was introduced showing that the van abandoned by Aldrete-Davila contained a large amount of marijuana. Although he denied knowing the exact quantity of the drugs he was carrying, Aldrete-Davila admitted that he was aware that he was transporting drugs and that he was committing a serious offense. Notwithstanding the arguments they now make, however, the record shows that the defendants in fact made specific arguments to the jury based on the large size of the load itself and Aldrete-Davila's possible motives. Thus, the specific weight and value of the marijuana load would have added little more to the case of the defense and reasonably could be seen as cumulative; Aldrete-Davila's admission of the seriousness of the offense and the evidence of the size of the load demonstrated the point that the defendants were attempting to show by this further evidence. The exclusion of this evidence certainly placed no Sixth Amendment limitation on the defense. Consequently, the district court's exclusion of the specific weight and size of the marijuana load was neither a Sixth Amendment violation nor an abuse of discretion relating to an evidentiary matter.

3.

a.
The second exclusion of evidence focuses on Aldrete-Davila's alleged involvement in a drug-trafficking incident  for which he had been neither convicted nor charged[3]  that occurred in October 2005, some eight months after the February incident.[4] Similar to their arguments relating to the size of the marijuana load, the defendants argue that this more extended involvement in drug trafficking makes it likely that he was lying about not knowing the details of the drug trade. Primarily, however, the evidence is relevant, it is argued, to show that Aldrete-Davila, as someone who was more than a one-time drug offender, likely possessed a gun on February 17. Although the focus of the defendants' argument is on restriction of cross-examining Aldrete-Davila, the defendants argue, second, that they should have been allowed to introduce independent evidence establishing this transaction for essentially the same reasons of relevancy. As we shall discuss, in addition to these two facets of the evidence relating to the October 2005 incident, the basis of the district court's exclusion of this evidence was also double-barreled: first, its relevancy was outweighed by its prejudice *450 and confusion and, secondly, the Fifth Amendment privilege asserted by Aldrete-Davila barred the subject from cross-examination.
The admissibility of this evidence was first raised prior to trial when the district court was asked to decide whether evidence of other drug activities should be admitted during the course of trial. The district court entered a pretrial order ruling that introducing such evidence would be confusing, misleading to the jury, and highly prejudicial to the conduct of the trial and would therefore not be allowed. See Fed.R.Evid. 403. In connection with the cross-examination of Aldrete-Davila, however, the court ruled that the defendants could inquire about Aldrete-Davila's other drug activities as related to his immunity agreement.
At trial, both Christopher Sanchez (who delivered and explained the immunity agreement to Aldrete-Davila) and Aldrete-Davila testified that the agreement protected Aldrete-Davila only from prosecution for crimes related to the events of February 17. Later, Aldrete-Davila testified on cross-examination that he had little knowledge regarding how drugs are packaged, or any significant knowledge of the logistics behind drug trafficking. Upon Aldrete-Davila's denial of such details, the defendants sought to cross-examine him concerning other alleged drug activities in which he may have been involved, both before and after the events of February 17. The defendants argued that such cross-examination was proper to test Aldrete-Davila's credibility; if Aldrete-Davila admitted to transporting drugs on another occasion, then an inference could be drawn that he had more knowledge about such matters as packaging drugs than he had previously claimed; thus his credibility would be compromised and the jury might be inclined to reject all of his testimony. The defendants admitted they had no knowledge of any such drug activities before February 17 but indicated that the government had disclosed some evidence of one incident occurring in October 2005. The court sustained the government's objections to such evidence, citing the lack of relevance to the issues of this trial.
This ruling did not end the matter, however. The defendants' later efforts to elicit this testimony from Aldrete-Davila were then countered by Aldrete-Davila's assertion of his Fifth Amendment right not to incriminate himself. It was at this point that the immunity agreement developed into a central controversy. The defendants strenuously argued that Aldrete-Davila could not assert a Fifth Amendment privilege because the immunity agreement extended to the October 2005 incident; alternatively, the defendants urged the court to grant immunity to Aldrete-Davila on its motion so that they could cross-examine him about the October incident. The district court noted the questionable relevance and highly prejudicial effect of such evidence on the conduct of the trial, stating at one point that it was not going to permit the case to devolve into a trial of the witness, Aldrete-Davila. Ultimately, in its last statement on the admissibility of cross-examination on the October incident, the court ruled that Aldrete-Davila's immunity agreement was only for the events of February 17 and that, as to the October incident, Aldrete-Davila could assert his Fifth Amendment right. Cross-examination on the October episode was then precluded.
Thus, we can see that the district court made its exclusionary ruling on Aldrete-Davila's other drug-trafficking activities on two bases. It ruled, on the strength of its understanding of Aldrete-Davila's immunity agreement, that Aldrete-Davila was entitled to assert his Fifth Amendment right *451 against self-incrimination. But this ruling paralleled another: evidence of other drug activities, in the context of the credibility question before it, might prove to be of some relevance, but because the evidence was so prejudicial to the trial of the case and so potentially confusing to the jury, its relevance was substantially outweighed by its prejudice and it could not be admitted.

b.

i.
We turn to what the defendants contend is the crucial mistake the district court made in its evidentiary ruling: they strenuously argue that the district court erred in allowing Aldrete-Davila to assert his Fifth Amendment privilege against self-incrimination. This argument requires us to consider in detail the immunity agreement itself, its words, its context, its legal characteristics, and its effect.
In the defendants' view, the immunity agreement with Aldrete-Davila clearly immunizes from prosecutorial use against Aldrete-Davila any and all testimony that he might give in the trial, including testimony relating to crimes that did not exist when the agreement was made.
As discussed above, the agreement has its origins in Special Agent Sanchez's visit with Aldrete-Davila in Mexico when Sanchez was seeking Aldrete-Davila's cooperation. When Aldrete-Davila signed the immunity agreement, Special Agent Sanchez orally explained to him that the agreement meant that he would not be prosecuted for the crimes he committed on February 17, so long as he testified truthfully.[5] Both Aldrete-Davila and Agent Sanchez testified that the immunity agreement was limited to the events of February 17. The government made similar representations at trial. As earlier noted, the defendants contend that the agreement applies to the October incident as well. Thus, the issue to be addressed is the proper interpretation of the immunity agreement between the U.S. Attorney and Aldrete-Davila.

ii.
General contract principles guide the interpretation of informal immunity agreements, which are, as here, immunity agreements that are not sanctioned by a court order. See United States v. Castaneda, 162 F.3d 832, 835 (5th Cir.1998); United States v. Pelletier, 898 F.2d 297, 301-02 (2d Cir.1990). The written immunity agreement between the U.S. Attorney and Aldrete-Davila is dated March 16, 2005 and its two central paragraphs read as follows:
In connection with your cooperation with the Department of Homeland Security, Office of the Inspector General, and any subsequent testimony before the Grand Jury sitting in the Western District of Texas, El Paso Division, and any subsequent hearing and/or trials:
1. The Government agrees to provide you with all of the protection which *452 would be provided to you under a formal court-ordered grant of immunity pursuant to the provisions of Title 18, United States Code, sections 6002 and 6003. In other words, no testimony or other information provided by you, or any information directly or indirectly derived from that testimony, or other information will be used against you in any criminal case in this district, provided you do not violate the terms of this agreement.
In interpreting this agreement, we begin with the first paragraph of the "letter-contract." This paragraph clearly addresses only the February 17 episode: it was signed by Aldrete-Davila in March when the only crime extant occurred on February 17, 2005. It refers to a sitting grand jury, language that would seem not to include future grand juries. Finally, it states that the agreement is being issued in connection with Aldrete-Davila's cooperation with the government, when his only possible cooperation would be with the only investigation being conducted by the government  that is, the investigation related to February 17. To state the obvious, the October episode had not yet occurred, and the U.S. Attorney could not have been seeking Aldrete-Davila's cooperation with respect to a crime occurring six months after the agreement was signed. To understand the agreement as a guarantee by the U.S. Attorney that, if Aldrete-Davila testified at a later date about crimes unknown to the government and not yet committed by Aldrete-Davila, the U.S. Attorney would not use that testimony and any of its derivatives against Aldrete-Davila, is quite unreasonable. See United States v. Irvine, 756 F.2d 708, 710 (9th Cir.1985) (noting that immunity agreements should be read to avoid "absurd results"); United States v. Brimberry, 779 F.2d 1339, 1346-47 (8th Cir.1985) ("Although there is broad language in the immunity agreement between Brimberry and the government, there is nothing in the agreement which supports an intention to grant Brimberry immunity to violate the law in the future."); United States v. Black, 776 F.2d 1321, 1328 (6th Cir.1985) ("It is too firmly established that grants of immunity do not license future criminal conduct to permit any other construction of the language in the [poorly-drafted] agreement.").
We now advance to the second paragraph of the immunity agreement, which describes the character of the grant of immunity: The immunity granted offers the same protection as described in §§ 6002 and 6003, which the paragraph then describes in the second sentence as use and derivative use immunity. See § 18 U.S.C. § 6002 ("[N]o testimony or other information compelled under the order (or any information directly or indirectly derived from such testimony or other information) may be used against the witness in any criminal case ....").
In sum, the first paragraph of the agreement describes the subject of the crime with respect to which immunity will be granted, while the second paragraph describes the nature of the immunity being granted. We think the conclusion is clear: Any information that Aldrete-Davila provides, or testimony he gives, relating to the crime of February 17, or any information derived therefrom, will not be used against him in any prosecution in the Western District of Texas.

iii.
The defendants argue, however, that the immunity agreement's reference to 18 U.S.C. §§ 6002 and 6003 requires a *453 different result.[6] These statutes reflect the means by which formal immunity is granted: the U.S. Attorney, with permission from the Attorney General or a designee, will apply for an order from the district court under § 6003, which, when granted, will provide a witness with use immunity; that is, the witness's testimony  and any derivatives  can never be used in a criminal prosecution of the witness.[7] The Supreme Court has held that a court order granting immunity under these statutes gives to a witness the same protection the Fifth Amendment provides; that is, when a court order is entered providing that a witness's statement, and information derived therefrom, cannot be used against him in a future criminal prosecution, he may not refuse to testify on the basis of his Fifth Amendment rights because the Fifth Amendment promises him no more rights than he has been granted by that court order. Kastigar v. United States, 406 U.S. 441, 453, 92 S.Ct. 1653, 32 L.Ed.2d 212 (1972).
But  and here is the crucial point under the facts of this case  Aldrete-Davila did not enjoy the benefits of immunity under the statute; or stated differently, the immunity granted Aldrete-Davila by the U.S. Attorney was not coextensive with the Fifth Amendment. The immunity agreement here, as all agree, was informal in nature.[8]
*454 As Kastigar made clear, for any grant of immunity to override the Fifth Amendment claim of a witness not to testify, the immunity granted must be coextensive with the protection the Fifth Amendment would otherwise give to that witness. See id. at 449, 92 S.Ct. 1653. The Fifth Amendment right is very broad: "It can be asserted in any proceeding, civil or criminal, administrative or judicial, investigatory or adjudicatory; and it protects against any disclosures which the witness reasonably believes could be used in a criminal prosecution or could lead to other evidence that might be so used." Id. at 444-45, 92 S.Ct. 1653 (footnote omitted). But the informal immunity agreement here cannot purport to offer that same level of protection, both because of its explicit language and the nature of an informal grant of immunity.
The agreement only immunizes Aldrete-Davila's testimony from use in a prosecution in the Western District of Texas: "[N]o testimony or other information provided by you, or any information directly or indirectly derived from that testimony, or other information will be used against you in any criminal case in this district...." (emphasis added). Cf. 18 U.S.C. § 6002 (prohibiting use of immunized testimony in "any criminal case" (emphasis added)). The immunity agreement, therefore, does not bar the use of Aldrete-Davila's testimony in a subsequent prosecution in another judicial district and by another U.S. Attorney. The agreement is therefore clearly not coextensive with Aldrete-Davila's rights under the Fifth Amendment, which he may assert in any criminal proceeding in the United States.[9] Irrespective of the language that limits the agreement to the Western District of Texas, the informal immunity agreement could not have been binding beyond the jurisdiction of the U.S. Attorney for the Western District of Texas, the signatory to the agreement. "Under settled precedent, one federal prosecutor cannot bind his or her counterpart in another district unless he or she has been given the authority." United States v. Roberson, 872 F.2d 597, 611 (5th Cir.1989). The defendants make no indication that the U.S. Attorney here had been given any authority  such as that necessary to secure immunity under *455 § 6003  to bind prosecutors in other districts. As such, the agreement is both facially and by nature not coextensive with the Fifth Amendment and accordingly fails to satisfy the requirement of Kastigar. The district court therefore did not err in allowing Aldrete-Davila to assert his rights under the Fifth Amendment as to the October drug-trafficking incident.[10]

c.
We turn now to address the district court's parallel ruling, that is, the probative value of evidence of Aldrete-Davila's other drug activity was "substantially outweighed by the danger of unfair prejudice, confusion of the issues and misleading the jury, and by considerations of undue delay and waste of time." See Fed. R.Evid. 403. Although the district court also applied this ruling in precluding the cross-examination we have just discussed, it also applied it to exclude the evidence from sources independent of Aldrete-Davila's testimony.
We remind the reader that the defendants made a proffer that, if they were allowed to call witnesses, they would show that in October 2005, a person reasonably identified as Aldrete-Davila had been involved in a drug-trafficking incident as a transporter of drugs to a stash house. We also noted earlier that the crucial factual issue of the trial was whether, as suggested by Ramos and Compean, Aldrete-Davila possessed a gun  which he denied  when he was fleeing from Ramos and Compean. We also noted that in his testimony, Aldrete-Davila allegedly gave the impression that he was not a real player in the drug business and testified, for example, that he was unfamiliar with the details of drug packaging and did not know what kind of drugs were in the van. Thus, for the purpose of challenging Aldrete-Davila's credibility on these matters, and to show him more involved in drug trafficking than he admitted  and likely therefore to be lying in denying possessing or brandishing a gun  the evidence of his involvement in the October incident was, it is argued, relevant. In a nutshell, the defendants argue that the evidence was probative in determining Aldrete-Davila's credibility.
Assuming that the defendants could have made their proposed showing, it is hardly a powerful or probative challenge to Aldrete-Davila's account of February 17. The evidence would show one incident a number of months later  not earlier  in which he was acting in a similar low-level position as a transporter of a load of drugs. And it would have shown no indication that he was carrying a weapon on this occasion. Thus, the evidence is not particularly probative of his drug-related experiences eight months earlier and does not show him more likely to have possessed a weapon when fleeing from the van in February. It certainly does not directly contradict any of Aldrete-Davila's testimony.[11]
*456 On the other hand, the grounds for excluding this testimony are substantial. Because Aldrete-Davila's identity and specific connection to the incident had not been established and because the record indicates that the evidence identifying Aldrete-Davila was not certain, Aldrete-Davila's guilt of a subsidiary, unadjudicated crime could quickly have become a mini-trial within the trial and a proxy for the defendants' guilt, a point relied on by the district court in excluding the evidence. Disputes relating to a completely different scenario involving another drug-trafficking episode  and the evidentiary disputes accompanying it  would assuredly have diverted the attention of the jury, confused the issues actually to be decided, and unfairly prejudiced the conduct of the trial. See Fed.R.Evid. 403. The district court therefore did not abuse its discretion in excluding the evidence under Fed.R.Evid. 403.
To conclude this discussion relating to the defendants' Sixth Amendment claims, the district court did not violate the defendants' Sixth Amendment rights nor did it abuse its discretion in excluding evidence of the October 2005 incident.

B.
Moving on from these Sixth Amendment issues, the defendants next focus on 18 U.S.C. § 924(c)(1)(A), arguing that § 924(c) cannot constitutionally be applied to police officers in their circumstances and that the indictment charging them with the § 924(c)(1)(A) violation was fatally defective. This issue was not raised below; our review is for plain error. See United States v. O'Banion, 943 F.2d 1422, 1432 (5th Cir.1991). See, e.g., United States v. Bourgeois, 423 F.3d 501, 506 (5th Cir.2005).

1.
The first argument advanced by the defendants is that application of 18 U.S.C. § 924(c) to them violates the Due Process Clause of the Fifth Amendment, as the former agents had no warning  either from the statutory language or from its previous application  that the statute could apply to law enforcement officers when carrying out their duties. Before analyzing the legal merit of this argument, an important preliminary point must be emphasized: whether 18 U.S.C. § 924(c) may be applied to officers otherwise acting lawfully in carrying out their duties is not the question before us. Thus, our analysis does not assume  and, indeed, because of the jury verdict, cannot assume  as the defendants would have it, that the defendants acted in self-defense or for the safety of others. Instead, in accordance with the jury verdict, our analysis of the applicability of § 924(c) must assume that they shot at, and wounded, Aldrete-Davila without lawful justification.[12] Whether the defendants were justified in shooting Aldrete-Davila is an issue no longer in play after the jury verdict that rejected the defendants' versions of the facts.
*457 The "fair warning" requirement protected by the Due Process Clause reflects the legal principle "that no man shall be held criminally responsible for conduct which he could not reasonably understand to be proscribed." United States v. Lanier, 520 U.S. 259, 265, 117 S.Ct. 1219, 137 L.Ed.2d 432 (1997) (internal quotation marks omitted). As such, "[t]here are three related manifestations" in which fair warning may be lacking: vagueness, ambiguity (and the accompanying rule of lenity), and novel judicial constructions of statutes. Id. at 266, 117 S.Ct. 1219. "In each of these guises, the touchstone is whether the statute, either standing alone or as construed, made it reasonably clear at the relevant time that the defendant's conduct was criminal." Id. at 267, 117 S.Ct. 1219.[13]
Section 924(c)(1)(A) states, in pertinent part:
any person who, during and in relation to any crime of violence or drug trafficking crime ... for which the person may be prosecuted in a court of the United States, uses or carries a firearm, or who, in furtherance of any such crime, possesses a firearm, shall, in addition to the punishment provided for such crime of violence or drug trafficking crime 
(i) be sentenced to a term of imprisonment of not less than 5 years;
(ii) if the firearm is brandished, be sentenced to a term of imprisonment of not less than 7 years; and
(iii) if the firearm is discharged, be sentenced to a term of imprisonment of not less than 10 years.[14]
The defendants cannot advance a persuasive textual argument supporting their fair warning claim; § 924(c)(1)(A) is applicable to "any person" and contains no language that law enforcement officers are excepted from its application. Furthermore, there is no question but that a police officer's unjustifiable shooting of a victim qualifies as a crime of violence; there is no question but that a police officer's shooting a victim who poses no physical threat to the safety of the officer or the public is unjustifiable; there is no question but that during this conduct each of the defendants used a firearm. The facts relating to these postulates were decided by the jury based upon credibility determinations that we, as an appellate court, may not disturb.
The defendants therefore advance the argument that the application of the statute to the facts of this case is novel, i.e., did not provide them with fair warning, because its application here frustrates the statute's legislative purpose, has no support in the cases of this circuit, and makes *458 for bad public policy.[15] But cases in our circuit have permitted application of § 924(c)(1)(A) to police officers. See, e.g., United States v. Williams, 343 F.3d 423 (5th Cir.2003); United States v. Winters 105 F.3d 200 (5th Cir.1997).
The defendants' attempt to distinguish these controlling cases assumes their version of the facts, specifically, that Aldrete-Davila posed a specific threat to their physical safety. As we have pointed out repeatedly, this view of the facts was rejected by the jury. Stripped of this element, the defendants' argument is essentially that § 924(c)(1)(A) cannot be applied to law enforcement officers unless those officers are engaged in particularly egregious conduct so as to place them completely outside their law enforcement duties and authority.
The cases in which § 924(c)(1)(A) has been applied appear to encompass the circumstances of this case. The fact of being on duty, for instance, has not prevented conviction of police officers under § 924(c)(1)(A). See, e.g., United States v. Contreras, 950 F.2d 232, 234-36 (5th Cir. 1991) (finding police officer liable under § 924(c)(1) when police officer pulled a car over and sexually assaulted one of the passengers while police officer was on duty). Indeed, police officers have been held liable under § 924(c)(1)(A) even when their illicit behavior is proximate to their duties. See, e.g., Williams, 343 F.3d at 429-30 (finding police officer liable for shooting suspect in the back after the suspect was handcuffed); Winters, 105 F.3d at 202 (holding prison guard liable under § 924(c) after prison guard pistol-whipped prisoner while prisoner was in custody and in handcuffs). These cases seem definitively to provide notice that § 924(c)(1)(A) has application whenever a law enforcement officer uses a firearm when he is committing a crime of violence against another. We cannot overrule our own precedents; only an en banc court can do that.
Here, whether to prosecute defendants Ramos and Compean under this statute was a matter of prosecutorial discretion; once a prosecutor decides to prosecute a law enforcement officer who has similarly used his weapon against a fleeing, suspected felon, the officer may stand trial for a violation of § 924(c). We can surely debate whether there is an intuitive distinction between a violent criminal or a drug trafficker using a gun during the course of their trade and a police officer using a gun against a fleeing felon; however, neither the statute nor the cases make such a distinction. Still yet, the Supreme Court of the United States has firmly established that the conduct with which Ramos and Compean were charged, and for which they were convicted by a jury of their peers, violates the Fourth Amendment rights of the fleeing felon if he poses no physical threat to the officers or danger to others. See Tennessee v. Garner, 471 U.S. 1, 4, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985).

2.
The defendants make a further argument attacking their § 924(c)(1)(A) conviction: *459 the indictment is fatally defective. The defendants argue that the statutory language of § 924(c)(1)(A) reaches "any person who ... uses or carries a firearm, or who, in furtherance of any such crime, possesses a firearm" (emphasis added). The indictment charges that both defendants "discharged a firearm ... during and in relation to a crime of violence" (emphasis added). Because the statute does not include "discharge" among its substantive elements, the defendants argue that they have been charged with, and convicted of, a crime that does not exist. The defendants failed to raise this argument before the district court, and the standard of review is therefore plain error. United States v. Hoover, 467 F.3d 496, 498 (5th Cir.2006).
The question thus raised is whether the indictment's use of the term "discharges" instead of the statutory word "uses" suffices to charge a crime under § 924(c)(1)(A). "We have previously stated that although an indictment must inform the defendant of every element of the crime of which he is accused, an indictment need not track statutory language." United States v. Boyd, 885 F.2d 246, 249 (5th Cir.1989). An indictment need not precisely track statutory language because the "basic purpose" of an indictment is "to inform a defendant of the charge against him." Hoover, 467 F.3d at 499. Thus, "`[t]o be sufficient, an indictment must conform to minimal constitutional standards, standards that are met where the indictment alleges every element of the crime charged and in such a way as to enable the accused to prepare his defense and to allow the accused to invoke the double jeopardy clause in a subsequent proceeding.'" Id. (quoting United States v. Partida, 385 F.3d 546, 554 (5th Cir. 2004)). Those minimal constitutional standards therefore do "`not compel a ritual of words.' The validity of an indictment is governed by practical, not technical considerations." United States v. Crow, 164 F.3d 229, 235 (5th Cir.1999) (internal citation omitted) (quoting United States v. Devoll, 39 F.3d 575, 579 (5th Cir.1994)).
Here, the term "discharge" is but a specific manner of use of the broad term "use." Indeed, in considering the various meanings of "use," the Supreme Court interpreted that term to include, "most obviously, firing or attempting to fire a firearm." Bailey v. United States, 516 U.S. 137, 148, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995). Defendants have not demonstrated how employing the term "discharge" failed to provide notice or otherwise charge a crime. There is no plain error here.

C.
The defendants next contend that their convictions should be reversed because the government tried its case in such a way that they were convicted, not for a crime, but for violating certain Border Patrol policies. To be sure, throughout the trial, repeated reference was made by the government to various Border Patrol policies. The referenced policies covered such matters as high-speed pursuits, reporting firearm discharges, preserving evidence, and the use of deadly force. The district court admitted this evidence as relevant to intent and knowledge of wrong-doing relating to the defendants' crimes. The defendants now argue that the government's constant references to and emphasis on the defendants' disregard of established policies had the effect of allowing the policies to become the issue of conviction instead of the real issue  whether substantive criminal law had been violated.
Again, the defendants did not raise this objection in the district court; our review is therefore for plain error. Johnson v. *460 United States, 520 U.S. 461, 467-68, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997). The defendants now rely primarily on United States v. Christo, 614 F.2d 486 (5th Cir. 1980), for their argument. But Christo is a different case; it is marked by a comprehensive misuse of civil regulations not present in this record.
In Christo, a bank manager was nominally indicted for misapplication of bank funds. But "the government's theory of misapplication of bank funds center[ed] upon violation of 12 U.S.C. § 375a ... a civil regulatory banking statute." Id. at 489. Directly connecting liability under § 375a with guilt under the criminal banking statute was the central thrust of the government's strategy: "[t]he indictment and government's case at trial contended that each overdraft ... amounted to a violation of 12 U.S.C. § 375a and that these violations constituted a criminal misapplication of bank funds under 18 U.S.C. § 656." Id. (emphasis added). The government therefore argued that the civil regulatory statute was coterminous with the criminal statute from the very beginning, including in the language of the indictment itself. And, still further, consideration of the civil statute was mandated by the district court in its jury instructions. Id. at 491. These instructions stated that, if the jury decided that the bank manager had made certain loans, it had further to decide whether those loans violated the civil regulatory statute. See id. The civil regulatory statute and substantive criminal statute in Christo were so intertwined as to lead the court to question the actual basis of the bank manager's conviction. See id. at 492.
The flaws in the Christo prosecution did not occur here. Before trial, the district court explicitly prohibited the government from making any statement implying that violation of Border Patrol policies could be considered illegal. And at trial, the government never suggested that violation of one of the policies was sufficient for conviction. Instead, the government only used the policies as evidence of the state of mind of the defendants for crimes of violence, which had no dependency on the policies for their definition, essence, or viability. Christo does not prohibit and subsequent cases explicitly permit use of such evidence for these or similar purposes. See, e.g., United States v. Butler, 429 F.3d 140, 150 (5th Cir.2005); United States v. Cordell, 912 F.2d 769, 777 (5th Cir.1990). Moreover, as in Butler, testimony in this case was elicited by the defendants to the effect that violation of Border Patrol policies was not identical to a violation of criminal law. 429 F.3d at 150.
Finally, unlike Christo, the jury here was not told that it had to decide whether the defendants violated the policies in order to establish criminal culpability. The district court repeatedly admonished the jury that it was only to consider guilt in terms of the crimes actually charged in the indictment. There is no plain error here.

D.

1.
We now turn to the convictions for obstruction of justice under the statute entitled "Tampering with a witness, victim, or informant." As we have earlier noted, the defendants failed to report to their supervisors the discharge of their firearms as required by the policies of the Border Patrol. Based upon this omission of their respective duties, both defendants were convicted for obstruction of justice under 18 U.S.C. § 1512(c)(1) and (2). Section 1512(c) provides that:
(c) Whoever corruptly 

*461 (1) alters, destroys, mutilates, or conceals a record, document, or other object, or attempts to do so, with the intent to impair the object's integrity or availability for use in an official proceeding; or
(2) otherwise obstructs, influences, or impedes any official proceeding, or attempts to do so,
shall be fined under this title or imprisoned not more than 20 years, or both.
It is of course plain from the statute that the charged omission must obstruct "an official proceeding." Thus, the question we address is whether the Border Patrol's internal investigation of alleged employee misconduct in failing to follow the agency's established policies concerning firearms is "an official proceeding" within the meaning of § 1512(c).[16]
"The objective of a court called upon to interpret a statute is to ascertain congressional intent and give effect to legislative will. The clearest indication of congressional intent is the words of the statute itself. When the language of a statute is unambiguous we must follow its plain meaning." Davis v. Johnson, 158 F.3d 806, 810 (5th Cir.1998) (internal citations and quotation marks omitted). "`The plainness or ambiguity of statutory language is determined by reference to the language itself, the specific context in which that language is used, and the *462 broader context of the statute as a whole.'" United States v. Guidry, 456 F.3d 493, 502 (5th Cir.2006) (quoting Robinson v. Shell Oil Co., 519 U.S. 337, 341, 117 S.Ct. 843, 136 L.Ed.2d 808 (1997)).

2.
We begin our analysis with a look at the statute as a whole. Section 1512 is titled "Tampering with a witness, victim, or an informant." It generally criminalizes a number of activities related to those enumerated in its title, including the killing of or use of physical force against a person involved in an official proceeding, § 1512(a)(1),(2); the use of intimidation or threat to interfere with official proceedings, § 1512(b); and the use of harassment to prevent participation in an official proceeding, the reporting of a crime, an arrest, or the commencement of prosecution, § 1512(d). As can plainly be seen, the statute is focused on incidents in which one person has exercised direct or indirect force or influence on another in order to corrupt some official proceeding; this focus is in keeping with the stated purpose of the statute: "[T]o enhance and protect the necessary role of crime victims and witnesses in the criminal justice process." Pub.L. No. 97-291, § 2, 96 Stat. 1248 (1982).
Next, we look at the specific section under which the government indicted and convicted the defendants, § 1512(c). This section of the statute was enacted as part of the Sarbanes-Oxley Act of 2002, Pub.L. No. 107-204, 116 Stat. 745 (2002), and codified in § 1512. Specifically, this provision was enacted under Title XI of Sarbanes-Oxley, titled "Corporate Fraud Accountability," see Pub.L. No. 107-204, 300, reflecting Sarbanes-Oxley's general targeting of corporate malfeasance.
Our review of the statute as a whole and its amendment by Sarbanes-Oxley  that is, legislation against mayhem, murder and intimidation in criminal proceedings and for the protection for witnesses and victims from such conduct and legislation directed against corporate fraud  indicate to us that Congress did not intend for "official proceedings" to include internal investigations into agency employee conduct.

3.
We are further convinced, based on the statutory definition and the contextual meaning of the term "official proceeding," that § 1512 does not apply to routine agency investigations of employee misconduct. The definition of "official proceeding" as used throughout § 1512 is found in § 1515(a)(1). The relevant definition for our purposes lies in § 1515(a)(1)(C), which, after referring to proceedings before federal judges, the grand jury and Congress, states that an "official proceeding" means "a proceeding before a Federal Government agency which is authorized by law." This definition of "official proceeding" is somewhat circular. The single word "proceeding," broadly defined and standing alone, encompasses meanings that could support its construal as either an investigation or as a hearing. See Black's Law Dictionary 1241 (8th ed.2004) (defining proceeding in relevant part as "3. An act or step that is part of a larger action" and "4. The business conducted by a court or other official body; a hearing," and also citing approvingly an understanding of "proceeding" as "much used to express the business done in courts"). But the use of the term in § 1515(a)(1)(C) indicates that a more formal sense of the term is correct in the context of § 1512. The definition provided in § 1515(a)(1)(C) uses the preposition "before" in connection with the term "Federal Government agency," which implies that an "official proceeding" involves some formal convocation of the agency in *463 which parties are directed to appear, instead of any informal investigation conducted by any member of the agency. Cf. § 1515(a)(1)(D) (defining "official proceeding" to include proceedings before "any insurance regulatory official or agency or any agent or examiner appointed by such official or agency" (emphasis added)).
Finally, "official proceeding" is consistently used throughout § 1512 in a manner that contemplates a formal environment in which persons are called to appear or produce documents. See, e.g., § 1512(a)(1)(A) (reaching "[w]hoever kills or attempts to kill another person, with intent to prevent the attendance or testimony of any person in an official proceeding"); § 1512(a)(2)(A) (reaching "[w]hoever uses physical force or the threat of physical force against any person, or attempts to do so, with intent to influence, delay, or prevent the testimony of any person in an official proceeding"). Thus, in all the instances in which the term "official proceeding" is actually used in § 1512, its sense is that of a hearing rather than simply any investigatory step taken by an agency. These considerations bring us to the conclusion that an internal, informal investigation, in its most preliminary stages, of employee violations of an agency policy is not an "official proceeding" within the meaning of § 1512(c).

4.
The government's arguments for a contrary conclusion are not compelling. The government argues that the structure of the statute shows that § 1512(c)(2) should be construed as a "catch-all" provision among references to more serious forms of obstruction and intimidation and therefore should be read broadly to reach the defendants' actions. But this argument fails to address our more specific point  that an internal agency investigation is not an official proceeding within the meaning of § 1512  and consequently the interpretation fixating to covered obstructive conduct (and not to the type of proceeding) is inapposite. And the government has provided no other authority that meaningfully supports its position.[17]
Although we are confident that the investigation here plainly was not an "official proceeding" within the meaning of the statute, it is at the very least an ambiguous term in a criminal statute, and any ambiguity leads to the same conclusion  *464 that § 1512 cannot be applied to the facts here. Such ambiguity and the absence of binding case law would require us to apply the rule of lenity. See United States v. Orellana, 405 F.3d 360, 370 (5th Cir.2005). The rule of lenity is generally applied as a last resort, where the meaning of a statute cannot be discerned after recourse to other available means of statutory construction. See id. at 371. Consequently, even if we were less confident in our interpretation of § 1512(c), we still could not say with certainty that Congress intended to criminalize an omission that interferes with a preliminary, routine, intra-departmental inquiry of the type here.[18] Thus, because we "resolve ambiguity in criminal statutes by construing such statutes narrowly," United States v. Marek, 238 F.3d 310, 327 (5th Cir.2001) (en banc), we alternatively hold that the rule of lenity requires the conclusion that "official proceeding" in § 1512(c) does not embrace the agency investigation at issue here. The convictions and sentences of the defendants under § 1512(c)  Counts 6, 7, 8, 9, and 10 of the indictment  for failing to report the discharge of their weapons, are therefore vacated.

E.
We turn now to the defendants' objections to the jury instructions issued by the district court relating to their convictions under 18 U.S.C. § 113, 18 U.S.C. § 924(c)(1)(A), and 18 U.S.C. § 242. These objections were not raised below. Our review is thus again for plain error. United States v. Fuchs, 467 F.3d 889, 900 (5th Cir.2006). "`Plain error occurs only when the instruction, considered as a whole, was so clearly erroneous as to result in the likelihood of a grave miscarriage of justice.'" United States v. Martin, 332 F.3d 827, 834 (5th Cir.2003) (quoting United States v. Lankford, 196 F.3d 563, 575 (5th Cir.1999)). In reviewing the instructions, we find that plain error is foreclosed because the instructions conform with our precedents.
The defendants have several complaints about the § 242 civil rights jury instructions. The defendants first argue that the district court defined "willfully" incorrectly. However, their complaint confuses the criminal mental state required by § 242 with the independent reasonableness analysis related to the use of force. In any event, their argument is foreclosed by United States v. Sipe, 388 F.3d 471, 480 & n. 21 (5th Cir.2004), in which we specifically approved of the instruction given here defining "willfully."
The defendants also argue that the burden of proof was either misplaced or omitted from the § 242 instructions. The instructions, however, expressly state that the government must prove all elements of § 242 beyond a reasonable doubt. That the district court did not repeat the government's burden of proof when it gave a more detailed explanation of the § 242 elements does not create plain error.
Nor does the district court's statement near the end of all of its instructions that the jury must generally "seek the truth" create a plain error. See United States v. Winn, 948 F.2d 145, 159-60 (5th Cir.1991). As in Winn, the district court repeatedly instructed the jury that it had to reach its conclusions beyond a reasonable doubt, and there is no indication from the defendants that the "seek the truth" reference here was uniquely injurious  certainly not on the level that the plain error standard requires. See id. at 160.
*465 The defendants argue that the § 242 jury instructions constructively amended the indictment by a brief reference to the reasonableness of force that police exercise in a custodial situation, a factual situation that was not charged in the indictment. This brief reference is not plain error; the defendants do not claim that their convictions were premised on anything other than evidence related to the force that may be used in self-defense or defense of another. See United States v. Phillips, 477 F.3d 215, 221 (5th Cir.2007). The evidence offered during trial was focused solely on this issue, that is, whether use of their weapons was justified for their safety or the safety of others; the government did not try its case on any other basis than that charged in the indictment. See United States v. Mitchell, 484 F.3d 762, 772 (5th Cir.2007). As a result, there is no plain error. See United States v. Longoria, 298 F.3d 367, 371 (5th Cir.2002).
Lastly, the defendants argue generally that the jury instructions did not adequately include their theory of defense. The jury instructions did explain the law relating to self-defense and defense of others, as well as the objective reasonableness standard necessary for the use of force. These instructions reflected the defendants' contention that, in firing their weapons, they were responding defensively to behavior by Aldrete-Davila that they perceived as threatening. To the extent that the defendants argue that the instructions could have better explicated the theory of the defense, they are not entitled to a preferred wording in the jury instructions. See United States v. Simmons, 374 F.3d 313, 319 (5th Cir.2004). And, while the instructions for the § 924(c)(1)(A) charges do not reference a theory of defense, they do make clear that conviction for the predicate offenses is required for conviction under § 924(c)(1)(A); the instructions for each of these predicate offenses, as discussed above, contained adequate theories of defense. See United States v. Natel, 812 F.2d 937, 942 (5th Cir.1987). In short, these instructions were not erroneous and certainly do not rise to the level of plain error.

F.
Finally, the defendants urge that the evidence was insufficient to sustain their convictions under the assault and civil rights statutes.[19] These arguments can be addressed in brief.
The defendants' argument here is one to which they repeatedly return: they were justified in firing upon Aldrete-Davila. But, once again, we must remind the defendants that the jury did not believe the defendants' testimony that Aldrete-Davila possessed an object in his hand. Aldrete-Davila's own testimony, the behavior of the defendants after the shooting, and the inconsistent testimony offered by both defendants and other Border Patrol agents allowed the jury to conclude that the defendants faced no credible threat and, consequently, there was no justification for their firing upon Aldrete-Davila. Although disputed, the evidence, taken in the light most favorable to the jury verdict, supports the scenario that Aldrete-Davila fled toward the Mexican border after Compean took a swing at him with his shotgun and that, while he was in flight, the defendants without provocation fired their weapons at him several times.


*466 V.
We conclude. For the most part, the trial of this case was about credibility, and although the jury could have gone either way, it chose not to believe the defendants' version of the crucial events of February 17. The trial of the case was conducted fairly and without reversible error. The exclusion of evidence relating to the size of the marijuana load and Aldrete-Davila's alleged involvement in drug-trafficking events of October 2005 did not violate the defendants' Sixth Amendment rights to present a complete defense nor did it deny them a proper cross-examination of a witness against them. They were denied no right of due process for lack of notice that § 924(c) could be applied to police officers while performing law enforcement duties. Nor was the § 924(c) indictment defective. Moreover, the defendants were properly convicted of substantive crimes, not for violating Border Patrol policies. In instructing the jury, no reversible errors were committed and, finally, the evidence fully supports the jury verdict. We therefore affirm the convictions for counts 1 through 5 and counts 11 and 12.
However, we reverse and vacate the convictions for obstruction of justice under § 1512(c)  counts 6 through 10 of the indictment  because the Border Patrol investigation was not an "official proceeding" within the meaning of the statute. We therefore remand for resentencing not inconsistent with this opinion.
AFFIRMED IN PART; REVERSED AND VACATED IN PART; and REMANDED FOR RESENTENCING.
NOTES
[1]  Count 1: 18 U.S.C. §§ 7(3), 113(a)(1) & (2) (Both Ramos and Compean)

Assault with Intent to Commit Murder, and Aiding and Abetting
Count 2: 18 U.S.C. §§ 113(a)(3) & (2) (Both)
Assault with a Dangerous Weapon and Aiding and Abetting
Count 3: 18 U.S.C. §§ 113(a)(6) & (2): (Both)
Assault with serious bodily injury and Aiding and Abetting
Count 4: 18 U.S.C. § 924(c)(1)(A) (Ramos)
Discharge of a Firearm in Commission of a Crime of Violence
Count 5: 18 U.S.C. § 924(c)(1)(A) (Compean)
Discharge of a Firearm in Commission of a Crime of Violence
Count 6: 18 U.S.C. § 1512(c)(1) (Compean)
Tampering with an Official Proceeding
Count 7: 18 U.S.C. § 1512(c)(2) (Compean)
Tampering with an Official Proceeding
Count 8: 18 U.S.C. § 1512(c)(2) (Both)
Tampering with an Official Proceeding
Count 9: 18 U.S.C. § 1512(c)(1) (Ramos)
Tampering with an Official Proceeding
Count 10: 18 U.S.C. § 1512(c)(1) (Compean)
Tampering with an Official Proceeding
Count 11: 18 U.S.C. § 242 (Compean)
Deprivation of Rights Under Color of Law
Count 12: 18 U.S.C. § 242 (Ramos)
Deprivation of Rights Under Color of Law
[2]  "In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence." U.S. Const. amend. VI.
[3]  Aldrete-Davila was eventually indicted for this incident.
[4]  The defendants, as discussed below, also make reference to questions that would probe any incidents that occurred before February 17, but admitted at trial that they had no evidence of any such incidents. With respect to the October episode, their oral proffer indicated that they would introduce evidence that Aldrete-Davila had been selected from a line-up with some, though not total, certainty as having transported a large load of marijuana to a stash house, and that the transporter had been identified as having a catheter. The evidence would have also shown that the marijuana load was in packaging similar to that used on February 17.
[5]  There is some confusion regarding whether Aldrete-Davila has been granted both use and transactional immunity and whether the letter grants the former while Special Agent Sanchez orally promised the latter. Transactional immunity prevents prosecution for crimes; use immunity prevents the use of testimony in prosecution for crimes. See United States v. Brown, 298 F.3d 392, 410 (5th Cir.2002). Based on the record, Aldrete-Davila appears to have been promised that he would not be prosecuted for crimes related to February 17 and that none of his testimony related to his activities of February 17 would be used against him in subsequent prosecutions of other crimes, if any. We need not choose between them, however, because the precise kind of immunity he received is not determinative in our analysis.
[6]  18 U.S.C. § 6002 states in full:

Whenever a witness refuses, on the basis of his privilege against self-incrimination, to testify or provide other information in a proceeding before or ancillary to 
(1) a court or grand jury of the United States,
(2) an agency of the United States, or
(3) either House of Congress, a joint committee of the two Houses, or a committee or a subcommittee of either House,
and the person presiding over the proceeding communicates to the witness an order issued under this title, the witness may not refuse to comply with the order on the basis of his privilege against self-incrimination; but no testimony or other information compelled under the order (or any information directly or indirectly derived from such testimony or other information) may be used against the witness in any criminal case, except a prosecution for perjury, giving a false statement, or otherwise failing to comply with the order.
18 U.S.C. § 6003 states in full:
(a) In the case of any individual who has been or may be called to testify or provide other information at any proceeding before or ancillary to a court of the United States or a grand jury of the United States, the United States district court for the judicial district in which the proceeding is or may be held shall issue, in accordance with subsection (b) of this section, upon the request of the United States attorney for such district, an order requiring such individual to give testimony or provide other information which he refuses to give or provide on the basis of his privilege against self-incrimination, such order to become effective as provided in section 6002 of this title.
(b) A United States attorney may, with the approval of the Attorney General, the Deputy Attorney General, the Associate Attorney General, or any designated Assistant Attorney General or Deputy Assistant Attorney General, request an order under subsection (a) of this section when in his judgment 
(1) the testimony or other information from such individual may be necessary to the public interest; and
(2) such individual has refused or is likely to refuse to testify or provide other information on the basis of his privilege against self-incrimination.
[7]  Exceptions are made for "perjury, giving a false statement, or otherwise failing to comply with the order." 18 U.S.C § 6002.
[8]  Formal grants of immunity under the immunity statutes are different in kind than informal immunity agreements. See Irvine, 756 F.2d at 711-12; Taylor v. Singletary, 148 F.3d 1276, 1283 n. 7 (11th Cir.1998). The former, as noted above, are creatures of statute and their issuance, by a court order that conforms to the statute, supersedes the Fifth Amendment privilege. Taylor, 148 F.3d at 1283 n. 7. In contrast, an informal immunity agreement is just that: an agreement between witness and government in which both parties receive mutual benefits. Id. A witness who testifies under an informal immunity agreement is not threatened with contempt for his failure to testify, but instead with losing the benefit of the bargain he or she struck with the government. Id. Witnesses with informal immunity agreements therefore do not abdicate their Fifth Amendment privilege when entering into the agreement; it is not until they testify that they give up the privilege. Id. Indeed, informally immunized witnesses cannot later preclude the use of their testimony in a subsequent trial, save in accordance with their agreement with the government. See id.
[9]  Generally speaking, a witness is entitled to invoke the Fifth Amendment when the witness reasonably fears self-incrimination. See United States v. D'Apice, 664 F.2d 75, 76 (5th Cir.1981). And we have held that where a witness was uncertain about the sincerity with which an informal immunity agreement was offered and about its jurisdictional scope, the witness was entitled to invoke the Fifth Amendment. Id. at 78. At most, the reference to the statutes creates an uncertainty about the extent of the immunity offered, thereby entitling Aldrete-Davila to invoke the Fifth Amendment. See id.; cf. United States v. Williams, 809 F.2d 1072, 1082 (5th Cir.1987) (holding informal agreement enforceable against the government to the same extent as a statutory grant when the U.S. Attorney had explicitly granted informal immunity pending statutory grant, the U.S. Attorney had moved the court to grant statutory immunity, the statutory immunity had been approved by the Department of Justice, the U.S. Attorney had represented that the informal agreement was intended to be identical in effect to the statute, and the only statutory element lacking was the actual issuance of a court order).
[10]  In the case in which a witness, under an informal immunity agreement, asserts his Fifth Amendment privilege as to some of the elicited testimony while testifying generally, the district court could entertain a motion to strike the testimony in its entirety, depending on the degree of prejudice to the defendant. There was no basis for such a motion here, given the district court's ruling under Fed. R.Evid. 403.
[11]  The defendants had a fair opportunity to undermine Aldrete-Davila's credibility and did so. Christopher Sanchez, the Border Patrol agent responsible for the investigation into the shooting, offered testimony that showed Aldrete-Davila to have been less than honest in his initial discussions regarding the incident, particularly in identifying who picked him up after he was shot. And the defendants were able to argue, based on the size of the marijuana load, that Aldrete-Davila was in fact a trusted member of a large drug operation.
[12]  The defendants insist, repeatedly, that "here, the discharge of firearms was, without question, in the midst of a `tense, uncertain, and rapidly-evolving' situation, no matter who is to be believed" (quoting Graham v. Connor, 490 U.S. 386, 397, 109 S.Ct. 1865, 104 L.Ed.2d 443 (1989)). But whether Aldrete-Davila turned toward the defendants with an object in his hand or simply ran empty-handed to Mexico and never turned was a key point of dispute at trial. A suspect who poses no physical threat while fleeing to reach the Mexican border does not present the tense situation and uncertainty that justifies the use of deadly force. This point was resolved by the jury against the agents.
[13]  Ramos argues that he was also deprived of fair warning with respect to his conviction under 18 U.S.C. § 242. Lanier requires only that a statute and its related case law make the illegality of certain actions apparent. And Ramos's argument here, like the defendants' arguments relating to their § 924(c)(1)(A) convictions, assumes that the events surrounding the shooting were as the defendants described them. The jury rejected their claim of a credible threat justifying their actions. There is little question that Ramos was on notice that shooting an individual who posed no threat was a violation of a constitutional right. See Tennessee v. Garner, 471 U.S. 1, 4, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985).
[14]  "Crime of violence" is defined in 18 U.S.C. § 924(c)(3) as any felony "that has as an element the use, attempted use, or threatened use of physical force against the person or property of another, or that by its nature, involves a substantial risk that physical force against the person or property of another may be used in the course of committing the offense." Neither defendant challenges the conviction on the grounds that the predicate crime committed by the defendants  assault within the special territorial jurisdiction of the United States, 18 U.S.C. § 113  is not a crime of violence.
[15]  The defendants very briefly refer to an Equal Protection challenge to the statute, saying that their contention is similar to their Due Process argument. They go on to argue that the statutory purpose is to encourage those committing crimes to leave their guns at home. It is therefore irrational to apply the statute to police officers who must bear weapons at all times. The defendants' argument ignores the amendment to the statute that was specifically intended to bring police officers within the statute's reach, see United States v. Rivera, 889 F.2d 1029, 1031 (11th Cir. 1989), and the statute's requirement that the use of a firearm be connected to a crime of violence. The Equal Protection challenge was not made in the district court. There is no plain error here.
[16]  The indictment charging Ramos and Compean asserts in Count Eight that the defendants

did knowingly corruptly obstruct, influence and impede an official proceeding ... by failing to report to appropriate authorities the discharging of a firearm, which obstructed and impeded a contemporaneous investigation of the facts and circumstances surrounding the shooting for use in an official proceeding, including an official inquiry by the appropriate authorities, for consideration by a federal grand jury and for consideration by a trial jury, among other proceedings, in violation of [18 U.S.C. § 1512(c)(2)].
Ramos and Compean were charged independently in Counts Nine and Ten. The counts charge that each defendant
did knowingly, corruptly alter, destroy, mutilate and conceal a record, document and object and did corruptly attempt to destroy, mutilate and conceal a record, document and object with the intent to impair the object's integrity and availability for use in an official proceeding ... [by] having an affirmative duty, pursuant to U.S. Border Patrol rules and regulations, to report the discharge of any firearm provided to him for his use in the capacity of a U.S. Border Patrol Agent, failed to report that he discharged his Beretta 40 caliber firearm when he shot at [Aldrete-Davila], which firearm had been provided to him by the U.S. Border Patrol for his official use, and which failure to report impeded the generation of a written report and document, preventing said report and document from being available in an official proceeding in violation of [18 U.S.C. § 1512(c)(1)].
The official proceeding that was obstructed is not specified in any count; the government apparently concedes that, based on the evidence adduced at trial, both defendants could and may have been convicted under the indictment on the grounds that their failure to report interfered with a Border Patrol investigation. But if such an investigation does not qualify under the statute, then the conviction must be set aside. Yates v. United States, 354 U.S. 298, 311, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957) (applying rule "which requires a verdict to be set aside in cases where the verdict is supportable on one ground, but not on another, and it is impossible to tell which ground the jury selected."), rev'd on other grounds by Burks v. United States, 437 U.S. 1, 98 S.Ct. 2141, 57 L.Ed.2d 1 (1978). The focus of the briefs and our focus is accordingly on such an investigation.
Compean does not specifically challenge his convictions under § 1512(c)(1) and (2) for his destruction of his spent shell casings. Nevertheless, because he suffered from the same error, his convictions under these counts (Counts 6 and 7) are similarly reversed. See United States v. Sylvester, 143 F.3d 923, 935 n. 12 (5th Cir.1998); United States v. Gray, 626 F.2d 494, 497 (5th Cir. 1980).
[17]  The government offers two appellate cases that construe "official proceeding" to mean agency investigations. But neither are apposite. United States v. Gonzalez, 922 F.2d 1044, 1055-56 (2d Cir. 1991), interpreted a specific venue provision of an earlier version of the statute. That provision included the term "official proceeding" in defining where a prosecution could be brought, and the court interpreted this term to be inclusive of a DEA investigation. Id. But it did so because the substantive criminal subsection, defined elsewhere in § 1512, contained no mention of an "official proceeding." See id. The court simply determined that the venue provision could not have been intended to narrow the reach of the substantive criminal subsection. See id. at 1056 (premising its interpretation of "official proceeding" on the "conjunction" of the two relevant statutory subsections). It is therefore of little applicability. The other case cited by the government is actually supportive of our holding. The court in United States v. Kelley, 36 F.3d 1118, 1127 (D.C.Cir. 1994), premised its holding that an investigation by the Inspector General of the United States Agency for International Development was a "proceeding" within the meaning of 18 U.S.C. § 1505 (and, by the agreement of the parties, § 1512) on the fact that the Inspector General had the power to "issue subpoenas and administer oaths." Id. As such, the investigation in that case constituted "more than a `mere police investigation.'" Id. (quoting United States v. Batten, 226 F.Supp. 492, 493 (D.D.C.1964)). Here, there is no indication that the Border Patrol investigation was anything more than a "mere police investigation."
[18]  We do not address whether an agency investigation may never constitute an "official proceeding." We only hold that the investigation here does not qualify.
[19]  Compean urges that the evidence was insufficient for his conviction under 18 U.S.C. § 924(c). His entire argument purports to be an incorporation of his co-defendant's argument, but Ramos does not raise § 924(c) sufficiency claims. As a result, Compean's sufficiency argument here is waived.
