
585 F.3d 453 (2009)
UNITED STATES of America, Appellee,
v.
Lorenzo CATALÁN-ROMAN and Hernaldo Medina-Villegas, Defendants-Appellants.
Nos. 06-1182, 06-1183.
United States Court of Appeals, First Circuit.
Heard December 3, 2008.
Decided October 23, 2009.
*456 Steven M. Potolsky for appellant Catalán-Roman.
David Abraham Silva for appellant Medina-Villegas.
Maria A. Dominguez-Victoriano and Thomas Klumper, Assistant United States Attorneys, with whom Rosa Emilia Rodriguez-Velez, United States Attorney, and Nelson Pérez-Sosa, Assistant United States Attorney, were on brief, for appellee.
Before BOUDIN, STAHL, and LIPEZ, Circuit Judges.
LIPEZ, Circuit Judge.
Appellants Lorenzo Catalán-Roman ("Catalán") and Hernaldo Medina-Villegas ("Medina") were convicted after a jury trial of several counts relating to a conspiracy to rob armored vehicles and the shooting death of an armored vehicle guard, Gilberto Rodríguez-Cabrera ("Rodríguez"), which occurred during a robbery committed in furtherance of the conspiracy.
This appeal requires us to consider Catalán's claim that his constitutional rights were violated when the district court prevented him from introducing extrinsic evidence to impeach a key government witness. In addition, Catalán challenges: 1) the court's denial of his request to sever his trial from that of Medina, 2) restrictions on cross-examination, and 3) its decision to quash a subpoena for the tax records of the victimized armored car company and its owner. He also challenges his convictions on counts two, eight, and nine on double jeopardy grounds.
Medina challenges: 1) the sufficiency of the evidence supporting the convictions on counts five and six (the carjacking charges) and eight (the murder charge), 2) the court's failure to allow him the opportunity for allocution before sentencing him to life imprisonment on the murder charge, and 3) the court's calculation of the guideline sentencing range on the murder charge.
The government concedes that the convictions on counts eight and nine violated double jeopardy. It also concedes that Medina must be re-sentenced on count eight because he was not allowed the opportunity to allocute for that count. After careful consideration, we reject appellants' other claims.


*457 I.
We recount the pertinent facts in the light most favorable to the jury's verdict. United States v. Cruz-Diaz, 550 F.3d 169, 171 (1st Cir.2008).

A. The November 30 Armed Robbery
On November 30, 2001, James Cruz-Matias ("Cruz"), an armored truck guard working for Ranger American Armored Services ("Ranger"), was robbed at gunpoint while making a delivery of cash for his employer to the Saulo D. Rodriguez Credit Union in Gurabo, Puerto Rico. That day, Cruz worked as the messenger in a two-man team. As such, he had to carry the cash from the truck to the bank. His co-worker, Eluber Torres-Alejandro ("Torres"), was the driver and remained inside the truck during the delivery. As Cruz carried a bag containing $180,000 toward the door of the credit union, a man who had been waiting by the credit union's ATM approached him, pointed a gun at his face, and demanded the money. Two other assailants then appeared, also pointing guns toward Cruz's head. Cruz gave them the money. Before leaving, one of the assailants took Cruz's pistol from its holster, cocked it, and pointed it at Cruz's face. Instead of pulling the trigger, the assailants left with the gun and the $180,000, fleeing the parking lot in a gray or blue Jeep Cherokee Laredo. Soon after the robbery, Gurabo municipal police recovered nearby a burned-out blue Cherokee Laredo that had been carjacked from its owner two days before the robbery. Six fingerprints matching Medina's were retrieved from a newspaper left near the ATM, where the first assailant had been waiting just before the robbery. At trial, Cruz identified Medina as the first assailant.

B. The March 6 Attempted Armed Robbery
On March 6, 2002, several men attempted to rob two Ranger guards. Torres was again working that day, acting this time as the messenger while his partner, Rodríguez, drove the truck. As Torres carried a bag containing $300,000 from the armored truck to the door of the Valenciano Credit Union in Juncos, Puerto Rico, a man appeared and walked towards him in the parking lot. The man made a gesture toward his waist, revealing a firearm tucked in his waistband. Torres and Rodríguez both pulled out their own weapons and pointed them towards the man, who had pulled out the pistol and managed to point it at Torres. Apparently realizing that he was outnumbered, the man turned and ran away. Torres saw a two-toned motorcycle and a blue Chevrolet Lumina depart from the parking lot.[1] At trial, Torres identified Catalán as the man who had walked toward him in the parking lot and flashed a weapon before fleeing.

C. The March 26 Carjacking
On March 26, 2002, while parked in his green Ford Explorer outside his daughter's house and talking with her, Armando Jula-Diaz ("Julía") was approached by two assailants, one of whom pointed a nickel-plated pistol at him and demanded he turn over the vehicle.[2] The two assailants stole the Explorer, along with a black, 9mm Glock pistol that Julía had kept in the glove compartment.


*458 D. The March 27 Armed Robbery and Murder
The next day, on March 27, 2002, Ranger guards Torres and Rodríguez were assigned to deliver $100,000 to the Saulo D. Rodríguez credit union in Gurabo. Torres, the driver, remained in the truck while Rodríguez, the messenger, exited with the money and walked towards the credit union. As Rodríguez approached the entrance, an assailant appeared and pointed a black, 9mm Glock pistol at his face and chest. A second assailant then appeared carrying a Beretta semi-automatic firearm. At trial, Torres identified the first assailant as Medina and the second as Catalán. Rodríguez raised his hands above his head in an act of surrender. As Catalán attempted to remove Rodríguez's firearm from its holster, Medina fired two shots at Rodríguez. Torres then opened the door of the armored truck and began firing at Catalán, who was hit and fell to the ground. Torres was shot in the left hand by a fourth indicted co-conspirator, Quester Sterling-Suarez ("Sterling"). Torres fell back into the truck and closed its doors.
Medina took the money and fled the scene in a green Ford Explorer, leaving the injured Catalán behind. Rodríguez was still alive at this point. According to Torres, Rodríguez pleaded for his life just before Catalán, seated on the ground nearby, picked up his Beretta firearm and fired it several times into him. Sterling then arrived and tried to help Catalán, but fled the scene alone when police arrived.[3] Catalán was apprehended at the scene, seriously wounded and still holding the Beretta. Rodríguez died soon thereafter, having received a total of eight gunshot wounds, three of which would have proven fatal even independent of the other wounds. One of the fatal wounds came from Medina's 9mm Glock (the gun that had been stolen from Jula the day before), while the other two came from Catalán's Beretta. At the scene, the FBI obtained shell casings, bullet fragments, and bullets that matched Catalán's Beretta and Medina's Glock. Not far from the credit union, police recovered Jula's stolen green Ford Explorer with its doors open, the engine running, and a small tank of gasoline nearby. Inside the vehicle, they recovered the stolen Glock 9mm pistol used by Medina during the robbery.
Shortly after the robbery, Morales picked up his girlfriend, Jocelyn Serrano-Castro ("Serrano"), in his blue Chevrolet Lumina. She spent the day with him, during which time he switched the car he was driving, retrieved a pistol hidden behind a highway mile marker, and conversed with a fifth co-conspirator, Pablo Sanchez-Rodríguez ("Sanchez"), about "getting rid" of the blue Lumina. At six o'clock that evening, Serrano observed Morales retrieve a sack of cash from Sanchez and buy new cell phones with some of the cash. Several days after the robbery, she went with Morales to visit appellant Medina at his home. Medina and his wife had bought all new furniture. Medina told Serrano that he had "scored a robbery and that they had to take everything out and bring in everything new."
The FBI arrested Medina on April 2, 2002. The vehicle Medina was driving at the time of his arrest had three newspaper articles about the March 27 robbery in the glove compartment. After his arrest, he was housed in the same prison cell as Miguel Alamo-Castro ("Alamo"). At trial, Alamo testified that while they were cellmates Medina had revealed several incriminating details about the conspiracy to rob Ranger vehicles. For example, Medina *459 told Alamo that he had carjacked a green Ford Explorer from a man and his daughter the night before the March 27 robbery, stealing a 9 mm Glock in the process. He said that he had participated in the shootout during the March 27 robbery and that the FBI had recovered the gun he had used from the seat of the stolen Explorer after the robbery. Medina also told Alamo that he was going to use the robbery money to buy furniture and remodel his home, among other things.

E. The Indictment and Trial
Approximately one year later, on March 14, 2003, a grand jury returned a ten-count second superseding indictment charging Catalán, Medina, Morales, Sterling, and Sanchez with conspiracy to rob armored vehicles and a number of substantive offenses related to the conspiracy. Specifically, both Catalán and Medina were charged with: conspiracy to commit robbery of an armored vehicle, in violation of 18 U.S.C. § 1951(b)(3) (count one), aiding and abetting the use of a firearm in relation to the conspiracy in count one, in violation of 18 U.S.C. §§ 2, 924(c)(1)(A)(iii) (count two),[4] aiding and abetting the March 27 robbery of an armored vehicle, in violation of 18 U.S.C. §§ 2, 1951(a) (count seven), aiding and abetting the use of a firearm to commit a crime of violence (the March 27 robbery) that resulted in the unlawful killing of Rodríguez, in violation of 18 U.S.C. §§ 2, 924(j) and 18 U.S.C. §§ 2, 1111 (count eight), and aiding and abetting the use of a firearm to commit a crime of violence (the March 27 robbery), in violation of 18 U.S.C. §§ 2, 924(c)(1)(A)(iii) (count nine). In addition, Medina was also charged with aiding and abetting the November 30, 2001 robbery of an armored vehicle in violation of 18 U.S.C. §§ 2, 1951(a) (count three), aiding and abetting the use of a firearm to commit the November 30 robbery, in violation of 18 U.S.C. §§ 2, 924(c)(3) (count four), aiding and abetting the March 26, 2002 carjacking, in violation of 18 U.S.C. §§ 2, 2119(1) (count five), and aiding and abetting the use of a firearm to commit the March 26 carjacking, in violation of 18 U.S.C. §§ 2, 924(c)(3) (count six). There were no charges based on the attempted robbery of March 6, 2002, nor was that attempted robbery cited as an overt act in furtherance of the conspiracy.
Jury selection began on January 25, 2005 and lasted thirteen days. Three days before trial, Catalán moved to exclude evidence that he was involved in the March 6, 2002 attempted robbery or, alternatively, for the severance of his trial from Medina's. He claimed that if the trials were severed, Medina would testify that Catalán had not been involved in the March 6 attempt. After an in camera conference with Medina's lawyer during which the lawyer made a proffer of his client's expected testimony, the court denied the motion.
Trial began on March 7, 2005. At the conclusion of the government's case, both appellants moved for judgment of acquittal pursuant to Federal Rule of Criminal Procedure 29. The district court denied their motions. At the start of appellants' case, the government moved to exclude the testimony of several witnesses whom the defendants intended to call to impeach the testimony of Torres, the armored car guard who was shot in the hand during the March 27 robbery. After hearing argument on the matter, the court granted the government's motion in part, excluding the *460 impeachment testimony of five law enforcement officers.
On March 16, government witness Juan Bravo-Hernandez ("Bravo") moved to quash a subpoena for tax records that had been issued at the request of defendants. Bravo, the president and owner of Ranger American Armored Services, had been subpoenaed to produce Ranger's corporate tax returns as well as his personal tax returns. The trial court granted the motion to quash, determining that the tax documents could not be relevant to the interstate nexus inquiry,[5] which had already been established through Bravo's testimony and could not possibly be affected by any information contained in either the company's or Bravo's own tax returns. After completing their evidence, appellants again moved for a judgment of acquittal, and the trial court again denied their motions. The jury found each appellant guilty of every count charged against him. Because the defendants had been previously certified as eligible for the death penalty, the trial then proceeded to the death penalty phase, which lasted fifteen days. The same jury that decided appellants' guilt decided whether to impose the death penalty. At the conclusion of the penalty phase evidence, the jury did not agree to impose the death penalty upon either defendant. 18 U.S.C.A. § 3593(e)(3). In special verdict forms, it asked the court to impose a sentence of life imprisonment without parole for Catalán and indicated that it could not agree to instruct the court to impose a life sentence for Medina.[6] Instead, the jury left Medina's sentence to the judge but indicated that it understood that the judge would impose a sentence of life imprisonment without parole. For count eight, the murder charge, the district court imposed on each defendant a sentence of life imprisonment without possibility of parole; it later also imposed sentences for each of the other convictions.

II.
We first confront Catalán's challenges to his convictions and sentence. Again, he challenges 1) the trial court's denial of his request to sever his trial from that of Medina, 2) the trial court's rulings restricting impeachment of Torres, including the court's decision to exclude extrinsic evidence that would allegedly impeach Torres's testimony, 3) the trial court's decision to quash the subpoena for tax records, and 4) the convictions on counts two, eight, and nine on double jeopardy grounds.

A. Severance
During jury selection, the defendants learned for the first time that the government planned to introduce testimony from Torres identifying Catalán as having been involved in the March 6 attempted robbery. Two-and-a-half weeks later, and four days before trial was to commence, Catalán moved to exclude the evidence, or alternatively, to sever his trial from that of Medina. He argued that if severance *461 were granted, Medina would testify that Catalán had not been involved in the March 6 attempt. However, if severance were not granted it would be unfair for the government to present Torres's testimony about Catalán's involvement, as Catalán would not be able to rebut that account through Medina's testimony. In a hearing on the motion, Medina's lawyer confirmed that his client would testify for Catalán if the trials were severed. Following the hearing, the judge held an in camera conference with Medina's lawyer, who made a proffer of his client's expected testimony. The court then denied the motion to exclude the evidence and the alternative motion for severance. Catalán now challenges the denial of his motion for severance.
We review the court's denial of a motion for severance for manifest abuse of discretion, United States v. DeCologero, 530 F.3d 36, 52 (1st Cir.2008), and affirm the lower court's decision unless the defendant makes a strong and convincing showing that prejudice resulted from the denial of severance, United States v. Richardson, 515 F.3d 74, 81 (1st Cir.2008). Defendants challenging the denial of severance must meet this high barrier on appeal because, as we have explained, in the normal course of events "[p]ersons who are indicted together should be tried together, since this practice helps both to prevent inconsistent verdicts and to conserve resources (judicial and prosecutorial)." United States v. Peña-Lora, 225 F.3d 17, 33 (1st Cir.2000) (quotation omitted).
In deciding the motion for severance based on the alleged need for the testimony of a co-defendant, district courts are to employ the two-tiered analysis set forth in United States v. Drougas, 748 F.2d 8, 19 (1st Cir.1984). To meet the first tier of that test, a defendant must demonstrate: "(1) a bona fide need for the testimony; (2) the substance of the testimony; (3) its exculpatory nature and effect; and (4) that the co-defendant will in fact testify if the cases are severed." United States v. Smith, 46 F.3d 1223, 1231 (1st Cir.1995). If the defendant can make that showing, the court should move on to the second tier of the Drougas analysis and "(1) examine the significance of the testimony in relation to the defendant's theory of defense; (2) consider whether the testimony would be subject to substantial, damaging impeachment; (3) assess the counter arguments of judicial economy; and (4) give weight to the timeliness of the motion." Smith, 46 F.3d at 1231.
Focusing on a first tier factor, the district court emphasized that Catalán had "failed to make a detailed proffer for this court to evaluate the exculpatory nature of [Medina's] testimony." Given that Catalán was not charged with the March 6 attempted robbery, a proffer about the evidence's "exculpatory nature" would have been especially important to the district court's analysis. This is particularly so because the focus of the government's case against Catalán, naturally, was on the overt act charged against him in the indictment: the March 27 robbery and murder of Rodríguez. The government's strong evidence of Catalán's involvement in that robbery and the general conspiracy to rob armored truck guards included damning physical evidence and testimony linking Catalán to the scene of Rodríguez's murder, where Catalán had assisted the robbery and was apprehended holding the murder weapon.[7] Without a detailed proffer *462 of the exculpatory nature of testimony about the March 6 attempted robbery, the district court was well within its discretion to conclude that Catalán had not shown a "bona fide need for the testimony." Smith, 46 F.3d at 1231.
Although it concluded that Catalán had not met the first tier of the Drougas analysis, the district court nonetheless proceeded to explain that he had also not met the second tier. In particular, the court emphasized the untimeliness of the motion, the highly impeachable nature of the testimony, and Catalán's lack of an explanation of the testimony's significance to his defense. Id.; see also, Smith, 46 F.3d at 1231 ("Judicial economy is obviously not dispositive, but it is important in a lengthy conspiracy trial."). There was no manifest abuse of discretion in the district court's denial of the motion.

B. Order to Quash the Subpoena for Tax Returns
Catalán objects to the district court's grant of Bravo's motion to quash a subpoena for his personal tax records and the tax records of his company, Ranger American Armored Security. A trial court may quash an "unreasonable or oppressive" subpoena, and we review the trial court's decision to quash for abuse of discretion. United States v. Henry, 482 F.3d 27, 30 (1st. Cir.2007).
The defendants were indicted under the Hobbs Act, 18 U.S.C. § 1951(a), which criminalizes robberies that have an effect on interstate commerce. United States v. Jiménez-Torres, 435 F.3d 3, 7 (1st Cir.2006). At trial, Bravo testified at length about the products his business regularly purchases from the mainland United States (such as specially equipped armored vehicles, weapons, and high-tech carrier's money bags). He also testified that the company was forced to pay high deductibles after each robbery, totaling $75,000, and explained that its insurer raised both its premium and deductible as a result of the robberies.
The defendants sought the personal and corporate tax records of Bravo and his company to challenge the government's assertion that the robberies affected interstate commerce. The trial court granted Bravo's motion to quash, determining that the tax records could not be relevant to the question whether the robbery sufficiently affected interstate commerce. In granting the motion, the court relied on this circuit's settled case law that a robbery need only have "a realistic probability of a de minimus effect on interstate commerce" to bring it within the reach of the Hobbs Act. United States v. Capozzi, 347 F.3d 327, 335 (1st Cir.2003) (quoting United States v. Butt, 955 F.2d 77, 80 n. 2 (1st Cir.1992)). "One common method for the government to establish the required `de minimis' effect on interstate commerce is to show that the defendant's activity `minimally depletes the assets of an entity doing business in interstate commerce.'" Capozzi, 347 F.3d at 337 (quoting United States v. Nguyen, 246 F.3d 52, 54 (1st. Cir.2001)).
We agree that Bravo's testimony about his company's participation in interstate commerce (including its regular purchases of carrier money bags, weapons, and vehicles from the United States), combined with his testimony about the financial effects *463 of the robberies, was sufficient to establish a de minimus effect on interstate commerce so as to bring the robberies within the reach of the Hobbs Act. We also agree that nothing in Bravo's personal or corporate tax returns could have negated the interstate nexus proven through Bravo's testimony, even if the company's bottom line was unchanged fromor, for that matter, even if it improved overthat of years past. See, e.g., Capozzi, 347 F.3d at 337 (de minimis effect established when defendant had threatened to extort $4,000 from a car dealer who participated in interstate commerce and a jury could have reasonably concluded that if the defendant had been successful the business's assets and purchasing power would have been at least temporarily depleted by $4,000). Therefore, there was no abuse of discretion in the district court's exercise of its power to quash unreasonable subpoenas.[8]

C. Restrictions on Impeachment[9]

1. Background
Catalán claims that his Sixth Amendment right to confront the witnesses against him and his Due Process rights were unconstitutionally impeded by the trial court's refusal to allow him to introduce extrinsic evidence that would have contradicted the testimony of the government's key eyewitness, Torres. Specifically, he argues that he should have been permitted to introduce the testimony of several FBI agents who would have impeached Torres's trial account of the robberies and the murder. Catalán claims that the agents' excluded testimony was "crucial to the defense theory" because he "wished to argue... that Torres Alejandro was unworthy of belief because (among other reasons) he dramatically changed his version of events very shortly before trial, adding new and highly aggravating details."
Catalán names five FBI agents whom he should have been allowed to call at trial. Agents Angel Marrero and María Cruz interviewed Torres shortly after the March 27 robbery, while he was in the hospital. Marrero and Cruz took notes of their interview in an official FBI FD-302 Form ("302"), a form for reporting and summarizing such an interview. United States v. Gonzalez-Melendez, 570 F.3d 1, 3 (1st Cir. 2009) (per curiam). The 302 of their interview, which purports to record Torres's account of the robbery, does not mention certain details which Torres gave in his trial testimony and which Catalán claims "were directly relevant to the government's theory of premeditation and death penalty." For example, the 302 does not mention that Rodríguez pleaded for his life and held up his arms to shield himself before Catalán shot him several times at "point blank range," or that Catalán glanced defiantly at Torres before taking that action.[10] Catalán argued below and *464 argues again on appeal that the agents' testimony about the March 27 incident would have undermined Torres's credibility through impeachment by omission, because Torres would not have left out such important details in his first interview if they were true. See, e.g., Jenkins v. Anderson, 447 U.S. 231, 239, 100 S.Ct. 2124, 65 L.Ed.2d 86 (1980) ("Common law traditionally has allowed witnesses to be impeached by their previous failure to state a fact in circumstances in which that fact naturally would have been asserted.").
Catalán also wished to call FBI Agents Francisco Ng and Félix Alvarado, who interviewed Torres after the November 30 robbery and also filed a 302 report. He argues that their testimony would have impeached Torres's trial account of the November 30 robbery. Whereas Torres testified at trial that he had not observed the November 30 robbery, Alvarado and Ng's report of their interview recounts that Torres had seen the robbery but had "frozen" and was unable to call for help. Contrary to his trial testimony, the report states that Torres did see the assailants, although it also states that he said he could not provide a good description of them.
Finally, Catalán claims that he should have been able to call Agent Carlos Marchand, the FBI's case agent, to impeach Torres's account of the March 27 robbery. Catalán claims that Agent Marchand would have testified that he had never heard certain details in Torres's trial account, such as that Rodríguez pleaded for his life before Catalán unloaded his pistol into him, until Torres testified at trial.
The trial court excluded the testimony of all five agents, ruling that it constituted impeachment by prior inconsistent statement through extrinsic evidence of a collateral matter and that the prior statements offered through agents Cruz and Marrero were not in fact inconsistent with Torres's trial testimony. However, Catalán was permitted to impeach Torres's credibility by extrinsic evidence of inconsistent statements through two other witnesses. He was permitted to call Carlos Bonilla-Rivera, a security investigator for Ranger American who recorded a statement from Torres after the November 30 robbery that was signed by Torres. In that statement, contrary to his trial testimony, Torres said that he saw, and was able to describe, one of the assailants. The defendants also called Agent Ríos-Calzada, who interviewed Torres after the March 6 robbery and took a written statement from him that was inconsistent with his trial testimony. The written statement was entered into evidence. The court provided no explanation for why these witnesses could be called for impeachment and not the others, except that Torres had signed the statements he made to the two witnesses and therefore he had "adopted" the statements.[11]
*465 On appeal, Catalán contests the court's decision to exclude the testimony of Agents Ng, Alvaredo, Cruz, Marrero, and Marchand.[12]

2. Catalán's Constitutional Claims
The Confrontation Clause of the Sixth Amendment protects a criminal defendant's right "to be confronted with the witnesses against him." U.S. Const. Amend. VI. Although the ability to pursue an impeaching line of inquiry with the introduction of extrinsic evidence supporting that inquiry might be viewed as part and parcel of the right to cross-examination, this circuit has yet to decide whether the Confrontation Clause provides defendants a right to impeach witnesses through extrinsic evidence. In White v. Coplan, 399 F.3d 18, 26 (1st Cir.2005), for example, a criminal defendant was found to have the right under the Confrontation Clause to cross-examine his accusers about false allegations they had made in the past, but the panel did not reach the question whether he had a right to introduce extrinsic evidence about those allegations. It was specifically noted that "cross-examination and extrinsic proof are two different issues." Id. at 25. The panel wrote that "we are not endorsing any open-ended constitutional right to offer extrinsic evidence [for impeachment purposes]. Such an excursion requires more witnesses and documents, and so greater risk of confusion and delay...." Id. at 26; see also Farley v. Lafler, 193 Fed.Appx. 543, 547 (6th Cir. 2006) (unpublished) ("The Supreme Court has not recognized the sweep of the Confrontation Clause to extend beyond guaranteeing the criminal defendant's right[ ] to physically confront and cross-examine adverse witnesses to encompass the right to impeach an adverse witness by putting on a third-party witness.") (quotation marks and citation omitted). Appellant makes no attempt to address White or otherwise explain specifically why the Confrontation Clause requires the introduction of the extrinsic evidence for impeachment purposes, and has therefore waived his conclusory Confrontation Clause argument. United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990).
However, as appellant points out, and the government acknowledges, "[w]hether rooted directly in the Due Process Clause of the Fourteenth Amendment, or in the Compulsory Process or Confrontation clauses of the Sixth Amendment, the Constitution guarantees criminal defendants `a meaningful opportunity to present a complete defense.'" Crane v. Kentucky, 476 U.S. 683, 690, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986). In Chambers v. Mississippi, 410 U.S. 284, 302, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973) (also cited by appellant in his brief), the Supreme Court recognized the constitutional dimension of a defendant's right to present witnesses in his defense, noting that "[f]ew rights are more fundamental." In Chambers, the excluded witnesses could have implicated a person other than the defendant, and their testimony *466 would have impeached that other person's denial of involvement in the crime. Id. at 292, 93 S.Ct. 1038. The exclusion of those witnesses infringed the defendant's due process right to "present witnesses in his own defense" and contributed to the denial of a constitutionally fair trial. Id. at 302-03, 93 S.Ct. 1038
Because appellant has cited Chambers and other Due Process cases, he has not waived that constitutional claim, and his complaint must be examined under the Due Process rubric. In that analysis, "[a] defendant's right to present relevant evidence is not unlimited, but rather is subject to reasonable restrictions." United States v. Scheffer, 523 U.S. 303, 308, 118 S.Ct. 1261, 140 L.Ed.2d 413 (1998);[13]see also Taylor v. Illinois, 484 U.S. 400, 410, 108 S.Ct. 646, 98 L.Ed.2d 798 (1988) ("The accused does not have an unfettered right to offer testimony that is incompetent, privileged, or otherwise inadmissible under standard rules of evidence."). Constitutional errors are reviewed for harmlessness beyond a reasonable doubt. Bembury v. Butler, 968 F.2d 1399, 1400 (1st Cir.1992).[14]

3. The Trial Court's Ruling on Inconsistency
The court ruled that the statement made by Torres at the hospital following the March 27 murder of Rodríguez, recorded in a 302 by agents Marerro and Cruz, was not inconsistent with Torres's trial testimony.[15] The court concluded that in light of Torres's injured condition at the time of the interview, the fact that he had taken pain medication, the short duration of the interview, and the fact that "we don't know what type of questions the agents asked," it would not have been "natural" for Torres *467 to include the aggravating details. See United States v. Meserve, 271 F.3d 314, 320-21 (1st Cir.2001) ("Prior statements... that omit details included in a witness's trial testimony are inconsistent if it would have been `natural' for the witness to include the details in the earlier statement."). The substance of defendants' proffer specifically stated, however, that Agent Cruz would testify that in her estimation Torres was an appropriate subject for an interview. Defense counsel proffered that Agent Cruz would testify as follows:
She would say that she recognized that he was in pain, that he had been shot, I think it was in the left hand, that she, in accordance with procedure and policy, took notes during the interview, that she recorded all of the important things that he said about the event, that the notes were effectively transcribed into a written report which ... she reviewed, initialed, as did Mr. Marrero, for accuracy.... She said that while he was in pain, in her opinion he was a subject for an interview. She did not feel that he was incapacitated or incapable of being interviewed and providing information. That during the interview itself, as he described the events that took place on March 27th, at no time during that interview did he indicate Mr. Rodríguez has his arms raised in a submissive mode prior to being shot. He did not at any time indicate that, prior to Mr. Rodríguez being shot, in the position with his arms raised, did he hear him say, please, no, please, no, please, no, and he did not indicate in any way that prior to that, in the mode with his hands raised, that the assailant, who he later identified in court as Mr. Hernaldo Medina Villegas, approached him from the front and shot him twice in the chest.[16]
Defense counsel also proffered that Agent Cruz had stated that she did not remember whether the interview was conducted in a question and answer format, or whether she had simply recorded Torres's narrative.
Unlike Meserve, on which the district court relied for its ruling that the omitted details were not inconsistent with Torres's trial testimony, the details omitted in Torres's earlier statement were not "peripheral" but went directly to the important element of premeditation as well as the possible imposition of the death penalty. Cf. Meserve, 271 F.3d at 321 (where "nuances [were] peripheral," district court did not abuse its discretion in excluding impeachment by omission through extrinsic evidence). As described in the discussion of the sufficiency of the evidence supporting Medina's conviction on the murder charge, see infra Part III(A), the indictment charged that the defendants had acted "with premeditation" in killing Rodríguez. With respect to premeditation, "it is the fact of deliberation, of second thought[,] that is important." United States v. Frappier, 807 F.2d 257, 261 (1st Cir. 1986) (citing Fisher v. United States, 328 U.S. 463, 469 n. 3, 66 S.Ct. 1318, 90 L.Ed. 1382 (1946)). The victim crying out for his life before he was shot by the defendant was some of the government's most persuasive evidence that Catalán had acted with premeditation in shooting Rodríguez.[17]
*468 Second, the impeachment was inconsistent in an important sense because the details that were essential to the government's death penalty case were left out of Torres's first interview. The same jury that decided the guilt phase was later asked to determine whether the death penalty was appropriate, and in doing so was specifically instructed that it could "consider any evidence that was presented during the guilt phase of the trial." In the penalty phase, the jury was asked to consider whether certain "statutory aggravating factors" applied to the crime. See 18 U.S.C. §§ 3591, 3592. These included whether the crime was committed in a "heinous, cruel or depraved manner," and whether the victim was vulnerable.
In the final analysis, the jury had to decide whether the murder of Rodríguez was a cold-blooded execution, or something else. Torres added several details at trial that went to that core issue and formed a central aspect of his narrative of the events of March 27, but which he had not mentioned in his earlier account. There was uncertainty about Torres's mental and physical condition at the time of the interview in the hospital, and the way in which the interview was conducted. Under these circumstances, it was an abuse of discretion for the court to determine that the crucial omissions in Marrero and Cruz's 302 report of their interview with Torres were "natural" and not inconsistent with his trial testimony. The significance of the omissions was a jury issue.[18]

4. The Trial Court's Collateral Fact Rulings
Under the common law of evidence and the law of this circuit, impeachment by extrinsic evidence is normally restricted to impeachment on matters that are not collateral. United States v. Cruz-Rodriguez, 541 F.3d 19, 30 (1st Cir.2008) ("`It is well established that a party may not present extrinsic evidence to impeach a witness by contradiction on a collateral matter.'") (quoting United States v. Beauchamp, 986 F.2d 1, 3 (1st Cir.1993)).[19] A matter is *469 considered collateral if "`the matter itself is not relevant in the litigation to establish a fact of consequence, i.e., not relevant for a purpose other than mere contradiction of the in-court testimony of the witness.'" Beauchamp, 986 F.2d at 4 (quoting 1 McCormick on Evidence § 45 (4th ed. 1992)).
The rule restricting impeachment to non-collateral matters is analogous to Rule 403's relevancy balancing test, which calls for relevant evidence to be excluded when its "probative value is substantially outweighed by ... considerations of undue delay, [or] waste of time...." Fed.R.Evid. 403; see also Beauchamp, 986 F.2d at 4. Although any demonstrated inconsistency in a witness's statement may impeach a witness's credibility, other concerns (such as wasting time and misleading the jury) become more important when the inconsistency at issue involves a statement relating to a matter that "`is not relevant in the litigation to establish a fact of consequence.'" Beauchamp, 986 F.2d at 4 (quoting 1 McCormick on Evidence § 45, 169 (4th ed. 1992)). On the other hand, when a statement that would be the subject of impeachment "is logically relevant to the merits of the case as well as the witness's credibility, it is worth the additional court time entailed in hearing extrinsic evidence." 1 McCormick on Evidence § 49 (6th ed. 2006).
Over defendants' protestations to the contrary, the trial court repeatedly ruled that evidence of Torres's prior inconsistent statements about the robberies was not admissible because it was "collateral." For example, in response to defendants' request to impeach Torres's claim that Rodríguez had pleaded for his life before being shot, the court said, "it's collateral source, collateral impeachment by extrinsic evidence because whether he said, no, no, oryes, yes ... that all doesn't go directly to the issues of guilt or innocence of the two defendants."
It is true that this circuit has said that "[i]n light of the collateral issue rule, in order to be admissible, ... testimony must not only contradict a statement ... but also be material to [the defendant's] guilt or innocence." United States v. Mulinelli-Navas, 111 F.3d 983, 988 (1st Cir.1997) (citing United States v. Payne, 102 F.3d 289, 295 (7th Cir.1996)). However, it appears that the district court may have interpreted that statementor one like itto mean that in order to be material here, the extrinsic evidence at issue must relate to whether the defendant did or did not shoot Rodríguez, or whether he stole the money, and not how the shooting or robbery were carried out.
This is too narrow a view. As has been noted, some of the details Catalán sought to impeachsuch as the defendants' and victim's behavior during the shooting plainly helped the government establish the premeditation that was charged as an aspect of the murder in count eight. Furthermore, several of the details were certainly relevant to the jury's consideration of the death penalty if the defendants were convicted.[20]See Kines v. Butterworth, 669 *470 F.2d at 6, 12 (1st Cir.1981). Torres was the only eyewitness to the March 27 murder of his partner, and was also a witness to and victim of the November 30 robbery. He had testified that the crimes were committed in a certain way, and the defendants sought to impeach him by introducing evidence through his prior inconsistent statements that the crimes were not committed that way. His accounts of the robberies and murder were unquestionably material to the government's case against Catalán, including its request for the death penalty, even if the impeachment of Torres on details of those accounts may not have exculpated Catalán from involvement in the crime.
Furthermore, Catalán argued below and argues on appeal that the trial court should have permitted the impeachment because it went to matters brought out on direct examination by the government, not through cross-examination by the defendant. That distinction is significant. The government's own belief that Torres's account of the details of the robberies and the murder were important supports the non-collateral nature of the inconsistencies identified by Catalán.[21]Cf. United States v. Sotomayor-Vázquez, 249 F.3d 1, 12 (1st Cir.2001) (despite the prohibitions of Rule 404(b), "[w]hen a defendant has, on direct examination, made a general denial of engaging in conduct material to the case, the prosecution may impeach that testimony by proving that the defendant did engage in that conduct on a prior occasion"). Finally, Catalán argues that exposure of the inconsistencies would have revealed Torres's motive to testify falsely: "fixing up all holes in the government's case, maximizing the chances in securing Puerto Rico's first death penalty verdict in modern times." This circuit has said that "a witness's... motive to testify falsely is generally considered to be a non-collateral issue." Beauchamp, 986 F.2d at 4.
For all of these reasons, the district court erred in excluding the testimony of the agents because of its view that their testimony dealt with a collateral matter.

5. Harmless Error
Both of the district court's rationales for excluding the impeachment testimony of the five government agentsthat some of the statements were not inconsistent and that all of the proffered testimony was collateralwere erroneous applications of the rules of evidence. However, "[v]iolation of a rule of evidence does not itself amount to a constitutional violation." Evans v. Verdini, 466 F.3d 141, 145 (1st Cir.2006). It is not necessary to decide whether the exclusion of the extrinsic evidence was an error of constitutional dimension. Under the circumstances of this case, even if there was a constitutional error, the error was harmless beyond a reasonable doubt. The evidence against Catalán was overwhelming: he was found wounded at the scene of the March 27 robbery and murder, holding one of the two murder weapons, and he was later *471 identified in court as the perpetrator. That inculpatory evidence would not have been impeached by the evidence that he sought to introduce through any of the agents. Furthermore, Catalán was permitted to impeach Torres's credibility by extrinsic evidence of inconsistent statements through Bonilla and Ríos, whose interviews with Torres following the November 30 and March 6 incidents differed from Torres's accounts at trial.
Of course, if Catalán had been sentenced to death, it might be necessary to decide whether the exclusion of the extrinsic evidence about the March 27 incident[22] was an error of constitutional dimension, because the harmless error analysis might well be different. As noted, in the penalty phase of the trial, the same jury that had decided appellants' guilt was asked to determine whether to impose the death penalty, and was expressly instructed that it could consider the evidence it heard in the guilt phase. Defense counsel expressed this concern at trial, arguing that if Torres's testimony went unimpeached, the defendants' lawyers would not later be able to "unring the bell" about the reprehensible details when it came time for the jury to deliberate about whether to impose the death penalty. That argument was apt, but, in the final analysis, the jury apparently did unring the bell.[23]

6. The Trial Court's Sua Sponte Comments
Catalán points to several portions in the trial transcript where the judge interrupted defense counsel, restricting or directing the course of defense counsel's examination. Catalán claims that these interruptions violated his Confrontation Clause right to cross-examine witnesses against him. After reading the excerpted portions of the transcript in context, it is clear that appellant's objections are groundless. In many places, the district court directed counsel on the proper way to conduct the examination; in others, the court reprimanded trial counsel for ignoring its earlier rulings. The court also interrupted the government's lawyers on occasion, and frequently sided with the defendants on objections. "It is well-established that a judge is not a mere umpire; he is the governor of the trial for the purpose of assuring its proper conduct, and has a perfect rightalbeit a right that should be exercised with careto participate actively in the trial proper." Logue v. Dore, 103 F.3d 1040, 1045 (1st Cir.1997) (quotation omitted). After careful consideration of the trial transcript, it is clear that the trial court overstepped no boundaries.

D. Double Jeopardy
Catalán claims that some of his convictions violated the Double Jeopardy Clause of the Fifth Amendment, which forbids punishing a person twice for the same offense. U.S. Const. amend. V. In Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 76 L.Ed. 306 (1932), the Supreme Court set forth the following test for determining whether multiple punishments for related offenses violate the Double *472 Jeopardy Clause: "where the same act or transaction constitutes a violation of two distinct statutory provisions, the test to be applied to determine whether there are two offenses or only one, is whether each provision requires proof of a fact which the other does not."
The government has sensibly conceded that the convictions for the offenses in counts eight and nine violated the Double Jeopardy Clause. Count nine set forth a violation of 18 U.S.C. § 924(c)(1)(A)(iii) for carrying a firearm in furtherance of the March 27 robbery. Count eight set forth a violation of 18 U.S.C. 924(j) for use of firearm during the March 27th robbery, which resulted in the death of Rodríguez. Count nine was a lesser included offense of count eight, as it did not require proof of any fact not required for conviction on count eight. See United States v. Jiménez-Torres, 435 F.3d 3, 10 (1st Cir.2006) (a § 924(c)(1) offense can be a lesser included offense of a § 924(j) offense).[24]
On the other hand, we reject Catalán's contention that his convictions on counts two and eight constitute a violation of double jeopardy. Because he did not raise this claim below, we review it for plain error. United States v. Winter, 70 F.3d 655, 659 (1st Cir.1995). Thus, Catalán must show that: 1) there was an error, 2) it was plain, 3) it affected a substantial right, and 4) it "seriously affect[ed] the fairness, integrity, or public reputation of judicial proceedings." United States v. Olano, 507 U.S. 725, 732, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993). The firearm conviction on count two is for the use of a firearm in connection with the overall conspiracy to rob armored vehicles (the count one conspiracy), whereas the firearm conviction on count eight is for use of a firearm in connection with the substantive robbery committed on March 27 (the count seven robbery). Therefore, counts two and nine each "require[ ] proof of a fact which the other does not." Blockburger, 284 U.S. at 304, 52 S.Ct. 180; cf. Marino, 277 F.3d at 39 ("[A] substantive RICO violation and a RICO conspiracy are not the same offense for double jeopardy purposes."). We therefore find no error, let alone plain error, in Catalán's conviction on count two.

III.
Appellant Medina challenges: 1) the sufficiency of the evidence supporting the conviction of count eight (the murder count), 2) the sufficiency of the evidence supporting the conviction of counts five and six (the carjacking counts), 3) the district court's failure to allow him the opportunity for allocution before being sentenced to life imprisonment on count eight, and 4) the district court's calculation of the guideline sentencing range on count eight.[25]


*473 A. Sufficiency of the Evidence
Before discussing Medina's specific challenges to the sufficiency of the evidence against him on counts five, six, and eight, we discuss a more general challenge that he apparently intends to make for all of the counts that charge him with "aiding and abetting" in the perpetration of a crime. He contends that he could not have been convicted of aiding and abetting because no "principal" was charged with and convicted of the crimes. Appellant's claim is based on a mistaken understanding of our law. "One who aids and abets a crime is punishable as a principal," United States v. Carlos Cruz, 352 F.3d 499, 507 (1st Cir.2003); see also 18 U.S.C. § 2, and "an aider and abettor in the commission of a federal offense may be convicted, although the principal had been acquitted of the offense charged." United States v. Cyr, 712 F.2d 729, 732 (1st Cir.1983) (citing Standefer v. United States, 447 U.S. 10, 20, 100 S.Ct. 1999, 64 L.Ed.2d 689 (1980)). While "[i]t is axiomatic that an aiding and abetting conviction requires proof that the substantive crime has been committed," Cyr, 712 F.2d at 732, there was overwhelming proof that the underlying crimesessentially robbery, use of firearms, carjacking, and murderwere committed. Among other evidence, there was testimony from Cruz, Torres, and Bravo which, taken together, detailed how armed assailants, pointing weapons, stole significant sums of cash from Ranger's guards on November 30, 2001 and March 27, 2002. Furthermore, Julía testified that his Ford Explorer was stolen from him by men pointing firearms at him, and the same Ford Explorer was later found abandoned with the engine running near the scene of the March 27 robbery. Julía's Glock, stolen along with the Explorer, was found inside the vehicle and had been fired several times during the robbery. Finally, and tragically, it is unquestionable that Rodríguez was gunned down on March 27 while performing his duties as a Ranger guard. The testimony of Torres, law enforcement officers who arrived at the scene, and forensics experts who examined the ballistics from the scene all consistently explain how Rodríguez was murdered in the course of the robbery. Simply put, there is nothing to appellant's claim that the evidence that any principal had actually committed these crimes was too thin for him to be convicted as an aider and abettor in the crimes.
More specifically, Medina also challenges the sufficiency of the evidence undergirding his convictions for carjacking (count five), use of a firearm during carjacking (count six), and the murder of Rodríguez (count eight). We review sufficiency of the evidence challenges de novo, "evaluating whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." United States v. Meléndez-Torres, 420 F.3d 45, 48-49 (1st Cir.2005) (internal quotation marks omitted).
Conviction for carjacking under 18 U.S.C. § 2119 requires the government to prove beyond a reasonable doubt that a defendant: 1) took or attempted to take from the person or presence of another, 2) a motor vehicle that had been "transported shipped, or received in interstate or foreign commerce," 3) with "force and violence or by intimidation", 4) with "intent to cause death or serious bodily harm." 18 *474 U.S.C. § 2119; United States v. García-Alvarez, 541 F.3d 8, 16 (1st. Cir.2008). A rational jury could have found each of those elements beyond a reasonable doubt. Julía testified that his green Ford Explorer was taken from him by two men on the night of March 26, 2002 and that one of the men pointed a nickel-plated pistol at Julía's face while demanding he exit the car. Co-conspirator Morales always carried a nickel-plated pistol. The same Ford Explorer, which the parties stipulated had traveled through interstate commerce, was found the next day near the scene of the robbery. Julía's Glock firearm, which had been in the glove compartment of the Ford Explorer when it was stolen, had been used during the robbery to shoot and kill Rodríguez. Torres identified Medina as the person who had used the Glock during the shootout. A government witness, Castro, testified that while he was a cellmate of Medina, Medina recounted his involvement in the carjacking as well as other crimes in the conspiracy.
There was also sufficient evidence to convict Medina on count six, the related offense of aiding and abetting the use of a firearm in conjunction with the carjacking. Again, Julía testified that the men who had stolen the car had pointed a nickel-plated pistol at his face.
Finally, there was sufficient evidence from which a rational jury could conclude that Medina was guilty of count eight, which charged that he aided and abetted the use of a firearm during a violent crime that unlawfully killed Rodríguez, with malice aforethought (as defined in 18 U.S.C. § 1111) "and with premeditation." "18 U.S.C. § 1111 `was intended to adopt the felony murder rule, and for a stated felony the `malice' element is satisfied by the intent to commit the unlawful felony.'" United States v. Morales-Machuca, 546 F.3d 13, 22 (1st Cir.2008) (quoting United States v. Shea, 211 F.3d 658, 674 (1st Cir.2000)). Therefore, murder that results from robbery is first degree murder. See 18 U.S.C. § 1111(a) ("Every murder ... committed in the perpetration of ... robbery ... is murder in the first degree."). Nonetheless, the indictment also charged that defendants acted with premeditation. "Premeditation" contemplates a temporal dimension, which need only be an "appreciable" amount of time; "it is the fact of deliberation, of second thought[,] that is important." Frappier, 807 F.2d at 261 (citing Fisher, 328 U.S. at 469 n. 3, 66 S.Ct. 1318). The judge instructed the jury that:
[P]remeditation is typically associated with killing in cold blood and require[s] the period of time in which the accused deliberates or thinks the matter over before acting. The law does not specify or require any exact period of time that must pass between the formation of the intent to kill and the killing itself. But it must be long enough for the killer after forming the intent to kill to be fully consc[ious] of that intent.
A reasonable jury could have found all of the elements of count eight beyond a reasonable doubt. First, Torres identified Medina as having fired the first of several shots at Rodríguez, while Rodríguez was on the ground with his arms raised and was not holding a weapon. Medina bragged to his prison cellmate, Alamo, that he had obtained a Glock with a laser from a carjacking which he later used in the March 27 shootout. Government experts explained that the Glock had been fired several times at the scene, and that at least one of its bullets hit Rodríguez and would have proven fatal even if Rodríguez had not also been wounded by Catalán's Berretta. Finally, Medina was in possession of several newspaper articles about the March 27 robbery at the time of his *475 arrest. There was sufficient evidence not only that Medina "aided and abetted" the violent felony that brought about the death of Rodríguez, but that he also shared with Catalán the primary responsibility for that death.
Based on this evidence, a rational jury could conclude that Medina is guilty of count eight as well as counts five and six. Therefore, we affirm all of the convictions against Medina.

B. Sentencing Challenges
Medina challenges the district court's failure to allow him the opportunity to allocute before sentencing him on count eight, the felony murder charge. Federal Rule of Criminal Procedure 32(i)(4)(A) requires that before imposing sentence a judge "address the defendant personally and ask the defendant if the defendant wishes to make a statement in the defendant's own behalf and to present any information in mitigation of punishment." Medina was not afforded that opportunity before being sentenced on count eight.
The government correctly concedes that Medina should be re-sentenced at a proceeding where he is present and afforded the opportunity to address the court. See United States v. Burgos-Andújar, 275 F.3d 23, 28 (1st Cir.2001) (due to the importance of Rule 32(i)(4)(A), which "reflects our long tradition of giving all defendants the right to directly address the court and plead for mercy," "if a sentencing court fails to provide a defendant with the chance to address the court, the reviewing court must remand the case for resentencing, generally without needing to inquire into prejudice."). Therefore, we vacate Medina's sentence on count eight and remand to the district court for re-sentencing. Because we remand for resentencing, we need not reach Medina's alternative argument that the district court failed to comply with the requirements of 18 U.S.C. § 3553(c).[26]

IV.
For the reasons set forth above, we vacate the conviction and sentence of appellant Catalán on count nine and further direct that the special assessment on that count be removed. We further vacate Medina's sentence on count eight and remand for resentencing. All other convictions and sentences are affirmed.
So ordered.
BOUDIN and STAHL, Circuit Judges, concurring.
Although we concur in the result and in most of what our colleague has written, our reasons differ from his in rejecting one of the principal claims of error. Among other claims raised on appeal, Lorenzo Catalán-Roman ("Catalán") challenges the district court's exclusion of testimony from FBI agents that he contends would have impeached Eluber Torres-Alejandro's ("Torres") testimony, most importantly, Torres' testimony about the robbery and murder on March 27, 2002. Our colleague believes there was error but that it was harmless; in our view no error was committed by the district judge.
Torres testified that Gilberto Rodríguez-Cabrera ("Rodríguez") had his hands in the air before any shots were fired, and that after Torres heard the first shot, Rodríguez fell backward, leaning against the front window of the credit union at which the robbery occurred; with his hands still *476 raised, Rodriguez then pleaded for his life before being shot by co-defendant Hernaldo Medina-Villegas ("Medina"); Rodríguez then fell to the ground wounded, after which Catalán shot him multiple times.[27] The allegedly inconsistent testimony that Catalán wanted to introduce was expected testimony from FBI agents, who interviewed Torres in the hospital, that Torres did not mention Rodríguez' raising of hands and pleading for his life.
The district judge said that the omissions were not inconsistent with Torres' court testimony (the court testimony added details but did not contradict the hospital statements) and, in addition, the hand raising and pleading (if they occurred) were merely "collateral" to the issues on trial and therefore not proper subjects for impeachment by extrinsic evidence. Under applicable evidence law, either rulingif correctwould justify excluding the testimony, 1 K. Broun, McCormick on Evidence §§ 34, 36, at 152, 156 (6th ed. 2006), but Catalán disputes both rulings, contending that his constitutional right to present a fair defense was impaired by mistaken evidentiary rulings.
Although Catalán cites constitutional precedent, such as Chambers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973), he does not develop any constitutional claim independent of his assertion that the court misapplied familiar federal common-law doctrine on impeachment by inconsistency and the collateral issue rule. Even if we assumed arguendo that errors in applying those rules were themselves constitutional errorhardly like to be so in all casesit would affect only the harmless error standard to be applied, Chapman v. California, 386 U.S. 18, 22-24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), and in this case we think there was no error by the district judge in finding the omissions not inconsistent with Torres' testimony.
Starting with the issue of inconsistency, the ordinary rule is that earlier omissions in reciting the same storyalthough not literally contradictions of later testimonycan be used to impeach a witness for inconsistency (on cross examination of the witness but not necessarily by extrinsic evidence) if the omitted information was not stated earlier "in circumstances in which that fact naturally would have been asserted." Jenkins v. Anderson, 447 U.S. 231, 239, 100 S.Ct. 2124, 65 L.Ed.2d 86 (1980); United States v. Meserve, 271 F.3d 314, 320-21 (1st Cir. 2001). Ordinarily, one might think that lurid details of the kind supplied in Torres' trial testimony might well have been supplied in the prior FBI interview; so, if they were not, this would allow, although it would not compel, an inference of inconsistency and so make the omissions relevant.
But the circumstances here were not ordinary. Torres was interviewed in the hospital, in pain and under medication; and while he was a critical witness, he was interviewed for only 15 to 20 minutes. Defense counsel asserted to the district court that one agent would testify that although Torres "was in pain," in her opinion he was not "incapacitated or incapable of being interviewed and providing information," but this does not mean that he was in the same condition as an ordinary witness or likely to be subject to the same degree or duration of questioning. Another agent testified (during co-defendant Medina's penalty phase) that such an interview usually *477 lasts several hours and that Torres' interview was "[o]bviously not" conducted under ideal circumstances.
In addition, the agents' main job was to find out who were the robbers and who had done the shooting. That Torres would likely have volunteered from his hospital bed details about raised hands and pleading is far from obvious, and so the supposed inference of inconsistency is of very doubtful force. There was no proffer by Catalán, and no reason to believe, that any agent was prepared to testify that Torres had been asked about raised hands, pleading or anything else focusing on these details and had denied such happenings. Absent inconsistency, the failure to mention the details had no impeachment value.
Although some trial judges might have left the matter to the jury, the district judge is entitled to make the threshold judgment as to inconsistency as an admissibility ruling, and such a call (like most other threshold admissibility rulings), is reviewed under an abuse of discretion standard. Meserve, 271 F.3d at 321. The trial judge found that in the circumstances it would not have been natural for Torres to add the details in question; and, given that admissibility depends not on any literal inconsistency but entirely on an inference about what a witness would likely have volunteered in these circumstances, we are not prepared to find an abuse of discretion here.
Likely the district judge would not have prevented Catalán from cross-examining Torres himself as to whether and why he had previously omitted details, and Catalán's counsel did ask Torres some questions about the March 27 interview with the FBI agents (although Torres largely testified only that he did not remember what happened in the interview). Typically, latitude is allowed in cross-examining the witness already on the stand whose reactions may be grist for the jury even without inconsistency. But before having other witnesses called, and trial time spent as well on exploring another dimension of Torres' medical condition, the district judge was entitled to insist on inconsistency and reasonably concluded that the omissions here did not qualify.
Although it does not affect the outcome as to the omissions in this case, a further limitation exists on the right to call a separate witness to testify to inconsistent statements: the traditional rule is that extrinsic evidence of prior inconsistent statements by the witness can be offered only if the earlier statements also were relevant to the substance of the case (in jargon, were "not collateral"). United States v. Cruz-Rodriguez, 541 F.3d 19, 30 (1st Cir.2008), cert. denied, ___ U.S. ___, 129 S.Ct. 1017, 173 L.Ed.2d 306 (2009); United States v. Beauchamp, 986 F.2d 1, 3-4 (1st Cir.1993). If so, the excursion required by extrinsic evidence is deemed worthwhile; otherwise, not.
Here, the indictment charged premeditationalthough it could have relied on felony murder instead, 18 U.S.C. § 1111(a) (2006)[28]and one might think that the supposed hand raising and pleading could bear on premeditation. But forensic evidence established that Catalán shot Rodríguez after the latter had already been *478 wounded by Medina, and Torres' testimony, unimpeached in this regard, merely confirmed this sequence of events. Shooting an already wounded man ordinarily meets the requirements of premeditationno particular interval is required, United States v. Brown, 518 F.2d 821, 826 (7th Cir.), cert. denied, 423 U.S. 917, 96 S.Ct. 225, 46 L.Ed.2d 146 (1975)so as to guilt it scarcely mattered whether Rodríguez had raised his hands and pleaded.
The lurid details about hand raising and pleading were relevantthat is, not collateralto the jury's further choice in the second phase of the trial as to whether to recommend death or life imprisonment. Thus, if the hospital-bed omissions were deemed inconsistent, extrinsic evidence of them would have to be allowed at that second stage. It is hard to imagine that at any penalty stage a judge would have excluded testimony bearing on the circumstances of the killing even if it consisted merely of Torres' failure to mention any details in an earlier interview.[29] In the event, the jury did not recommend the death penalty and the judge made clear his own default position was life imprisonment.
A more direct contradiction, about which Catalán also complains, concerns Torres' testimony about the earlier robbery on November 30, 2001. At trial, Torres testified that he did not observe the November 30 robbery or the assailants; earlier, it appears, two other FBI agents had interviewed him about the robbery and he told the FBI agents (according to their notes) that he saw the robbery but "froze" and could not call for help and that he saw the assailants but could not describe them. At trial Catalán sought to have the agents testify to the inconsistency, but the trial judge ruled it a collateral issue.
If Torres did make the earlier statements, they were certainly inconsistent and so went to his credibility, but (as already noted) this permits impeachment only through cross examination and not by extrinsic evidence unless the contradiction is material to the merits of the case. Here, it is hard to see how the contradiction is of any assistance to Catalán on the merits. He was not charged with participation in the November 30 robbery, and neither version of Torres' testimonythe one offered at trial or the one given earlier to the agentsimplicated Catalán in that robbery. Nor does Catalán offer in his brief any explanation beyond saying that the two versions contradict one another which goes only to credibility and not to the subject matter of the case.
Catalán also claims that, beyond impeaching the specific facts in Torres' testimony, the excluded FBI agent testimony in both instances also would have demonstrated Torres' bias and improper motive in testifying, and so was not collateral. But this is not so and the claim is not persuasively explained; the excluded testimony did not establish what Torres' bias and improper motive were, it merely contradicted certain details in Torres' version of events. Nor did Catalán make this bias or motive argument in the district court: he argued only that Torres' testimony was inconsistent and Torres therefore not credible; the new ground is not only unsupported but forfeit. Fed.R.Evid. 103(a); United States v. Olano, 507 U.S. 725, 731, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993).
Accordingly, we conclude that with respect to the claimed evidentiary errors, the *479 district judge permissibly excluded the extrinsic evidence in question. Harmless error doctrine happens to produce the same result in this case, but it is important to future cases that governing evidence law be reaffirmed. Trials are full of such evidentiary rulings, often made under pressure, and those made here were within the province of the trial judge.
NOTES
[1]  David Morales-Machuca ("Morales"), an indicted co-conspirator, drove a blue Chevy Lumina, and Medina drove a two-toned motorcycle.
[2]  According to Morales's ex-girlfriend, who testified at trial, Morales always carried a nickel-plated pistol.
[3]  Sterling was quickly apprehended.
[4]  18 U.S.C. § 2, included in all of the aiding and abetting charges, makes it illegal to aid and abet the commission of a federal offense.
[5]  18 U.S.C. § 1951, under which appellants were charged, criminalizes only those robberies which "obstruct[], delay[], or affect[]" interstate commerce. 18 U.S.C. § 1951(b)(3). See infra Part II(B).
[6]  Under the Federal Death Penalty Act of 1994, 18 U.S.C. § 3591 et seq., "[u]pon a recommendation under section 3593(e) that the defendant should be sentenced to death or life imprisonment without possibility of release, the court shall sentence the defendant accordingly. Otherwise, the court shall impose any lesser sentence that is authorized by law." 18 U.S.C. § 3594; see also Jones v. United States, 527 U.S. 373, 377-79, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999) (describing jury's role in imposing death penalty pursuant to the Federal Death Penalty Act).
[7]  Beyond asserting that Torres's testimony about the March 6 incident was "highly beneficial to the government on the issues of premeditation and participation in the conspiracy," Catalán does not develop an argument that, if the jury were to disbelieve Torres that Catalán was involved in the March 6 attempt, the substantial evidence of his participation in the March 27 robbery would have been insufficient to convict him of the conspiracy (count one) or aiding and abetting the use of a firearm in furtherance of the conspiracy (count two). Because this argument is not developed "beyond a cursory mention," Cao v. Puerto Rico, 525 F.3d 112, 114 n. 2 (1st Cir.2008), we deem it to be waived.
[8]  Catalán also complains that the district court's order quashing the Bravo subpoena denied him his Sixth Amendment right "to have compulsory process for obtaining witnesses in his favor." U.S. Const. Amend. VI. This constitutional claim was not raised at trial, and we therefore review it for plain error. United States v. Rodríguez-Lozada, 558 F.3d 29, 38 (1st. Cir.2009). Given our view about the minimal relevance of the tax records to the interstate commerce element of the Hobbs Act charges, there was no denial of Catalán's constitutional right to have compulsory process for obtaining witnesses in his favor.
[9]  The discussion from section C.1 through section C.5 reflects the views of the writing judge only. My colleagues express their separate views in the concurrence that follows this opinion.
[10]  In his brief, Catalán also claims that Agents Marrero and Cruz would have been able to impeach Torres's trial account of the March 6 attempted robbery. As far as can be discerned from the record (appellant gives us no citations other than an unidentified quotation, and the agents' report is not included in the record), this is a misleading statement of the evidence. At no time during the extensive discussions and arguments over this matter during trialnot even when the defendants made a proffer about Agent Cruz's testimonywas it suggested that Marrero or Cruz had ever discussed the March 6 attempt with Torres. The record does indicate, however, that FBI agent José Rios Calzada conducted an interview of Torres after the March 6 attempt and that Torres's account of the attempt was different during that interview than it was at trial. Nonetheless, the defendants were permitted to call him to the stand and, for purposes of impeachment, they entered the 302 report of the interview into evidence. See discussion infra.
[11]  That distinction has no basis in the rules of evidence or the common law of impeachment. "Any form of statement is acceptable" for impeachment by prior inconsistent statement. 1 McCormick on Evidence § 34 at n. 5 (6th ed. 2006). Federal Rule of Evidence 613(b) only requires that the impeached witness be "afforded an opportunity to explain or deny the [prior statement] and the opposite party [be] afforded the opportunity to interrogate the witness thereon," and has no requirement that the witness have adopted the prior statement.
[12]  The government argues that two of the five witnesses "would have possibly presented cumulative testimony." Cruz and Marrero would presumably have given similar testimony, as would Ng and Alvarado. See Fed. R.Evid. 403 (relevant evidence may be excluded, among other reasons, if it constitutes "needless presentation of cumulative evidence."). For reasons discussed below, it is not crucial that this contention be resolved.
[13]  In Scheffer, the Court wrote that:

A defendant's right to present relevant evidence is not unlimited, but rather is subject to reasonable restrictions. A defendant's interest in presenting such evidence may thus bow to accommodate other legitimate interests in the criminal trial process. As a result, state and federal rulemakers have broad latitude under the Constitution to establish rules excluding evidence from criminal trials. Such rules do not abridge an accused's right to present a defense so long as they are not arbitrary or disproportionate to the purposes they are designed to serve. Moreover, we have found the exclusion of relevant evidence to be unconstitutionally arbitrary or disproportionate only where it has infringed upon a weighty interest of the accused.
Id. (quotation marks and citations omitted).
[14]  The government argues that "[s]ince the defendant failed to raise some of [the] specific claims or arguments at trial or below, the Court reviews the claims for plain error." The government's only specific contention in this regard is that Catalán did not raise the argument that the impeachment would expose Torres's bias or motive to testify, which, in the words of Catalán, was to "fix[ ] up all holes in the government's case, maximizing the chances in securing Puerto Rico's first death penalty verdict in modern times." However, appellant argued below:

The defense gets to say to the jury ... are these details things that would be left out... if they really happened? Or are these details that are being added on later to make it a better death penalty case? That's our right to argue....
Although the issue is close, appellant's bias and motive argument is treated as having been properly raised. In addition to arguing that it would expose bias and motive, appellant unquestionably made the argument below that the impeachment would call into doubt Torres's credibility generally in the sense that, for whatever reason, he testified at trial to inflammatory details about the robberies and murder that he had not mentioned during prior interviews.
[15]  The court offered this ruling as a supplemental basis for exclusion of the impeachment, after making its ruling on the collateral fact issue. See infra Part II(c)(4). This issue is discussed first, however, because it is the logical antecedent of the ruling that the impeachment was collateral.
[16]  Although it is not included in the proffer, later discussions among the parties make clear that the 302 also recorded that Torres described a second shooter who, while wounded on the ground, fired several shots at the victim. However, this account of the second shooter, presumably Catalán, did not include the details of concern to appellant.
[17]  The government could have secured a first degree murder conviction without specifically charging premeditation, see 18 U.S.C. § 1111(a), but it nonetheless included premeditation in the charge on count eight as an element of the charged offense. The judge instructed the jury that it must find both malice aforethought as well as premeditation in order to convict the defendants. Although the defendants were charged with "aiding and abetting" the commission of the murder in count eight, that charge did not lessen the mental state required to convict appellant of the murder charge. Even under the aiding and abetting theory of liability, the government was required to prove that Catalán "consciously shared" the principal's intent. United States v. Mangual-Corchado, 139 F.3d 34, 44 (1st Cir.1998) (an aiding and abetting murder conviction "required proof beyond a reasonable doubt that Cirilo, before the murder occurred, consciously shared [the principal's] intention to kill Meijas and sought to ensure the success of the criminal enterprise....").
[18]  See 1 McCormick on Evidence § 34 (6th ed. 2006):

[W]hat degree of inconsistency between the witness's testimony and his previous statement is required? ... The test ought to be: Could the jury reasonably find that a witness who believed the truth of the facts testified to would be unlikely to make a prior statement of this tenor? ... Instead of restricting the use of prior statements by a mechanical test of inconsistency, in case of doubt the courts should lean toward receiving such statements to aid in evaluating the testimony. After all, the pretrial statements were made when memory was fresher and when there was less time for the play of bias. Thus, they are often more trustworthy than the testimony.
[19]  But see 1 McCormick on Evidence § 49 (6th ed. 2006) ("Given Rule 402 [which provides that "all relevant evidence is admissible"], there is a powerful argument that the collateral fact rule was impliedly repealed by enactment of the Federal Rules. Under this reading of the Federal Rules, there is no rigid prohibition on introducing extrinsic evidence to impeach a witness on a collateral matter; rather, under Rule 403, the judge would make a practical judgment as to whether the importance of the witness's testimony and the impeachment warrants the expenditure of the additional trial time. However, the collateral fact rule was so ingrained at common law that many federal opinions continue to mention `collateral' evidence."). This circuit continues to apply the collateral fact rule. See, e.g., Cruz-Rodriguez, 541 F.3d at 30; United States v. Marino, 277 F.3d 11, 24 (1st Cir. 2002).
[20]  Because it is not necessary to this decision, the significance, if any, of the fact that Agents Ng and Alvarado would have testified about a robbery for which appellant was not charged (the November 30 robbery) is not addressed.
[21]  However, this is not to suggest that testimony elicited on direct is always or automatically impeachable. See, e.g., Charles Alan Wright & Victor James Gold, 27 Fed. Prac. & Proc. Evid. § 6096 (2d ed. 2005) ("Some older authority suggests that the collateral matter doctrine applies only when the testimony to be contradicted was elicited on cross-examination. Under this approach, when a witness testifies to facts during direct examination she may be impeached by extrinsic evidence even if those facts are collateral. More recent authority and commentary rejects this approach, reasoning that contradiction as to a trivial matter wastes time and confuses the issues no matter whether the contradiction occurs on direct or cross examination.").
[22]  The desired impeachment through agents Ng and Alvarado was not relevant to the March 27 murder.
[23]  Strangely, Catalán apparently did not seek to have any of the agents testify about Torres's out-of-court account of the March 27 robbery and murder during the penalty phase of the trial, even though the court clearly took a different view of the relevance of the evidence in that phase of the trial. For example, it allowed co-defendant Medina to present previously excluded impeachment by extrinsic evidence through Agent Marchand during Medina's penalty-phase case. (Catalán's penalty-phase case preceded Medina's.)
[24]  Oddly, counsel for Medina has not also argued that Medina's convictions on counts eight and nine violate double jeopardy. Although in exceptional circumstances we may address arguments not raised by counsel, see United States v. Atkinson, 297 U.S. 157, 160, 56 S.Ct. 391, 80 L.Ed. 555 (1936), those circumstances are very rare and not present here. Other than a $100 special assessment imposed for count nine, Medina's conviction on count nine does not and cannot affect his sentence, which is life imprisonment.
[25]  In his pro se supplemental brief, Medina also argues that his "conviction[s] and sentences on all counts must be vacated as the evidence was legally insufficient." However, while he presents detailed arguments about the insufficiency of the evidence for counts five, six, and eight, he does not even mention the other counts, let alone explain why the evidence was insufficient. Even affording him a more lenient standard because he is pro se on these claims, see, e.g., Johnson v. Rodriguez, 943 F.2d 104, 107 (1st Cir.1991), this argumentation is insufficient to bring the sufficiency of the evidence for claims one through four and seven before us. Zannino, 895 F.2d at 17.
[26]  18 U.S.C. § 3553(c) requires a sentencing court to "state in open court the reasons for its imposition of the particular sentence...."
[27]  There is some discrepancy between the testimony, both as we read it and in the description of it given in the briefs, as to just when the hand raising occurred; we have chosen the version that seems to be best supported, but the differences are not material to the outcome.
[28]  Count eight of the second superseding indictment charged Catalán under 18 U.S.C. §§ 2, 924(j) with aiding and abetting the use of a firearm to cause the death of a person in the course of a crime of violence, specifically, a robbery. Section 924(j)(1) cross-references 18 U.S.C. § 1111 and provides that if the killing is "murder (as defined in section 1111)," the perpetrator shall "be punished by death or by imprisonment for any term of years or for life." 18 U.S.C. § 924(j)(1). The indictment also explicitly cross-referenced the definition of murder in section 1111.
[29]  There is no indication that Catalán sought to introduce the supposed omissions at the penalty phase, and the judge permitted codefendant Medina to introduce in the penalty phase testimony from Agent Carlos Marchand on the omissions in Torres' prior statements about March 27.
