
608 F.3d 654 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Alonso AYON CORRALES, Defendant-Appellant.
No. 09-3259.
United States Court of Appeals, Tenth Circuit.
June 14, 2010.
*655 Kirk Redmond, Assistant Federal Public Defender, (Cyd Gilman, Federal Public Defender, with him on the brief), Kansas City, Kansas, for Defendant-Appellant.
Jared S. Maag, Special Assistant United States Attorney, (Lanny D. Welch, United States Attorney), Topeka, Kansas, for Plaintiff-Appellee.
Before HARTZ, BALDOCK, and GORSUCH, Circuit Judges.
HARTZ, Circuit Judge.
A jury in the United States District Court for the District of Kansas convicted Alonso Ayon Corrales of possession of cocaine with intent to distribute and conspiracy to possess cocaine with intent to distribute. See 21 U.S.C. §§ 841, 846. He appeals, raising two contentions: First, he argues that the district court should not have instructed the jury that it could find the knowledge element of his two offenses by finding deliberate ignorance, because there was insufficient evidence of deliberate ignorance. Second, he argues that the district court violated his rights under the Confrontation Clause by improperly restricting his cross-examination of his accomplice, Ricardo Padilla. We have jurisdiction under 28 U.S.C. § 1291 and affirm.
We need not address the first contention because Mr. Corrales does not challenge the sufficiency of the evidence to support a jury finding that he had actual knowledge of the presence of cocaine. And we reject his Confrontation Clause contention because (1) he has not argued that the district court erred on the two occasions on which it sustained objections to his cross-examination of Padilla and (2) he has failed to show that the cross-examination was otherwise limited.

I. BACKGROUND
On July 20, 2005, Deputy Kelly Schneider of the Russell County, Kansas, Sheriff's Department stopped a speeding car driven by Ana Villano. Mr. Corrales was the sole passenger. During the stop Schneider became suspicious of drug-trafficking activity for several reasons. First, the vehicle's ownership had recently been transferred several times (Villano told him that she *656 and Mr. Corrales had just purchased it, and documents showed that Heriberto Rodriguez had purchased it on May 22, 2005, and sold it on June 20 to Ricardo Padilla). Second, Villano's hands were shaking badly. Third, although Villano stated that she and Mr. Corrales were married, Schneider did not see a wedding ring on Mr. Corrales. Fourth, although Villano told him that they were traveling from Modesto, California, to Atlanta, Georgia, where they intended to visit their family for about five days, the shortest route would have been through Oklahoma, not Kansas. Finally, Schneider noted a road atlas and two cell phones, which he associated with drug trafficking.
Schneider asked Villano for permission to search the car, and she consented. Eventually, cocaine was found in a secret compartment. Schneider arrested Villano and Mr. Corrales, who were then interviewed. Mr. Corrales said that he lived in Modesto and planned to travel to Durham, North Carolina, and then visit a friend named Arturo in Atlanta. He had borrowed the car from a friend named Ricardo because his own car was in disrepair. Although he said that he had known Ricardo for two years, he could not recall his last name until the officer suggested that it was Padilla (the name on an ownership document). He stated that once he arrived in Durham he was to call one of two numbers that Padilla had written on the atlas recovered from the car and tell the person who answered that he had Padilla's car. Someone he did not know would pick up the car from him and return it after an undetermined period of time. Mr. Corrales acknowledged that this arrangement was strange. After leaving North Carolina he and Villano were to go to Atlanta to stay with someone named Arturo whose address was written by Padilla on the atlas in the car.
Neither Mr. Corrales nor Villano was charged at the time. But two years later, on July 18, 2007, Mr. Corrales, Padilla, and Rodriguez (who ostensibly had sold the car to Padilla) were indicted on drug charges arising out of the stop. In the meantime, Padilla had been involved in another drug offense. Three months before the Kansas indictment he had been arrested at a California border crossing while attempting to enter the United States in a pickup truck containing methamphetamine and cocaine. He pleaded guilty to that offense on October 30, 2007, and on March 3, 2009, he pleaded guilty in Kansas as part of a plea agreement that required him to testify against Mr. Corrales.
Trial of Mr. Corrales began on April 29, 2009. Law-enforcement officers testified to the above-described statements by Villano and Mr. Corrales and the contents of their car. In addition, Padilla testified. He said that Rodriguez, the father of his oldest sister, had asked him to smuggle drugs from Mexico and transport them to North Carolina, and that Rodriguez had provided the car in which the drugs were hidden. After crossing the border with the drugs, however, he panicked and called Rodriguez to back out. Rodriguez attempted to calm him down, but when he again refused to make the trip to North Carolina, Rodriguez gave him a number to call and instructed him to deliver the car to the person who answered. The man who answered told him to take the car to Modesto, where he again called the man, who gave him directions to a gas station. When Padilla called from the station, another car quickly pulled up and an occupant signaled that Padilla should follow. He followed the car to a nearby house and left the car with Mr. Corrales, who drove Padilla to his home in Yuba City, California. Padilla also testified that he did not recognize Villano, did not write anything in the road atlas in the car, and did not know *657 an Arturo in Atlanta. And he said that neither Rodriguez nor Mr. Corrales was involved in his 2007 offense. Mr. Corrales did not testify.

II. DISCUSSION

A. Jury Instruction
Mr. Corrales was convicted of possession of cocaine with intent to distribute, see 21 U.S.C. § 841, and conspiracy to possess cocaine with intent to distribute, see id. § 846. The elements of the possession offense are (1) possession of cocaine, (2) knowledge of that possession, and (3) intent to distribute the cocaine. See United States v. Dozal, 173 F.3d 787, 797 (10th Cir. 1999). The elements of conspiracy are "(1) an agreement with another person to violate the law, (2) knowledge of the essential objectives of the conspiracy, (3) knowing and voluntary involvement, and (4) interdependence among the alleged conspirators." Id. (internal quotation marks omitted). Thus, knowledge is an element of both offenses.
The jury instruction on the meaning of knowledge addressed both actual knowledge and deliberate ignorance:
The term "knowingly," means that the act was done voluntarily and intentionally, and not because of mistake or accident. Although knowledge on the part of the defendant cannot be established merely by demonstrating that the defendant was negligent, careless, or foolish, knowledge can be inferred if the defendant deliberately blinded himself to the existence of a fact. Knowledge can be inferred if the defendant was aware of a high probability that controlled substances were in the vehicle in which he was stopped, unless the defendant did not actually believe controlled substances were in that vehicle.
R., Vol. 1 at 57. The instruction was taken from 10th Circuit, Criminal Pattern Jury Instruction No. 1.37 (KnowinglyDeliberate Ignorance) (2005 ed.).
Mr. Corrales's challenge to the instruction is not that it misstates the law. Rather, he contends that there was insufficient evidence at trial to support a jury finding of deliberate ignorance, so an instruction on that theory was improper. He is correct that the instruction should not be given absent supporting evidence. In United States v. Hilliard, 31 F.3d 1509 (10th Cir.1994), we wrote: "The use of a deliberate ignorance instruction is appropriate only when evidence has been presented showing the defendant purposely contrived to avoid learning the truth." Id. at 1514 (internal quotation marks omitted).
Nevertheless, we need not determine in this case whether there was sufficient evidence of deliberate ignorance. Mr. Corrales does not challenge the sufficiency of the evidence to support a conviction based on a finding of actual knowledge. And when there is sufficient evidence to support a conviction on one theory of guilt on which the jury was properly instructed, we will not reverse the conviction on the ground that there was insufficient evidence to convict on an alternative ground on which the jury was instructed.
This proposition was set forth by the Supreme Court in Griffin v. United States, 502 U.S. 46, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991). Diane Griffin was indicted for conspiring to defraud the government. The conspiracy allegedly had two objects: "(1) impairing the efforts of the Internal Revenue Service (IRS) to ascertain income taxes; and (2) impairing the efforts of the Drug Enforcement Administration (DEA) to ascertain forfeitable assets." Id. at 47, 112 S.Ct. 466. The evidence at trial was sufficient to support a conviction on the *658 IRS object of the alleged conspiracy, but not the DEA object. See id. at 47-48, 112 S.Ct. 466. Despite her request that the jury be instructed that she could be convicted only if it found that she was aware of the IRS object, "[t]he court instructed the jury in a manner that would permit it to return a guilty verdict ... if it found her to have participated in either one of the two objects of the conspiracy." Id. at 48, 112 S.Ct. 466. Griffin was convicted. The Supreme Court affirmed, ruling that when an offense can be committed by two or more means, a guilty verdict will be sustained when the evidence is sufficient to support one of the means, even if the evidence will not support any alternative means. See id. at 50, 57, 112 S.Ct. 466. The Court reasoned that when faced with facts supporting one of the theories of conviction but not the other, jurors, relying on "their own intelligence," are "well equipped to analyze the evidence." Id. at 59, 112 S.Ct. 466. The Court noted that the result is different when the jury is improperly instructed on a legally inadequate theory (such as an instruction that misstates the elements of a crime), because in such cases jurors "are not generally equipped to determine whether a particular theory of conviction submitted to them is contrary to law." Id.
We have applied Griffin in a situation almost identical to that before us. In United States v. Hanzlicek, 187 F.3d 1228, 1233 (10th Cir.1999), we held that there was sufficient evidence to support a deliberate-ignorance instruction in a fraud prosecution. But we went on to say, following Griffin, that even if there was not sufficient evidence, "a district court does not commit reversible error where it submits a properly-defined, although factually unsupported, legal theory to the jury along with a properly supported basis of liability." Id. at 1236.
Griffin and Hanzlicek control the result here. Because there was indisputably sufficient evidence for the jury to find that Mr. Corrales had actual knowledge, and because there is no suggestion that the knowledge instruction misstated the law, we must reject Mr. Corrales's challenge based on the deliberate-ignorance theory stated in the instruction.

B. Cross-examination of Padilla
Mr. Corrales argues that the district court violated his constitutional right to confront the witnesses against him by restricting the cross-examination of his coconspirator Padilla. See Delaware v. Van Arsdall, 475 U.S. 673, 678, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986) (Confrontation Clause protects a right to cross-examination). He complains that he was not able to question Padilla fully about Padilla's smuggling offense in 2007, two years after Mr. Corrales's offense. We reject the complaint because Mr. Corrales has not shown that the district court restricted the cross-examination of Padilla on that subject.
Mr. Corrales's brief on appeal cites to only one occasion in the record when the district court allegedly excluded evidence regarding Padilla's 2007 offense. That occasion was at the outset of trial. On April 30, 2009, Mr. Corrales's attorney moved to dismiss the charges with prejudice because he had not been informed until that morning of Padilla's conviction for smuggling drugs in 2007 at the California border with Mexico. He claimed that the delay in disclosure prevented him from investigating the 2007 offense to obtain not just impeachment evidence but also evidence admissible under Fed.R.Evid. 404(b) ("Other crimes, wrongs, or acts") to show that Padilla is "a drug dealer that would be predisposed to try to trick somebody like [Mr. Corrales] into doing the dirty *659 work once he gets the load over the border, which we know now he does on a regular basis." R., Vol. 2 Part 1 at 71. Counsel cited United States v. Montelongo, 420 F.3d 1169 (10th Cir.2005), which reversed a drug conviction because the trial court had excluded evidence of a similar offense committed by a government witness.
The district court denied the motion, noting that the record revealed that defense counsel had been informed by April 21, 2009, that Padilla had a prior drug conviction. Also, referring to Montelongo, the court said that it "has no present intention of precluding the Defendant from cross-examining Mr. Padilla about his California conviction or the events that gave rise to it," R., Vol. 2 Part 1 at 37-38, and added that this case was distinguishable from Montelongo anyway because Padilla's two offenses were not sufficiently similar for the 2007 offense to qualify as Rule 404(b) evidence. Mr. Corrales's attorney responded that he was concerned that the court was making a preliminary ruling under Rule 404(b) and therefore requested an opportunity to submit a brief on the matter. The court granted the request.
Thus, the district-court ruling cited by Mr. Corrales as limiting his cross-examination of Padilla was far from a definitive ban. First, the court said that it intended to permit cross-examination of Padilla regarding the 2007 offense and the underlying events. Second, to the extent that the court commented on Rule 404(b) when ruling on the motion to dismiss, it said that it would consider further briefing on the matter.
The following morning defense counsel submitted a brief in support of his motion to dismiss. The brief addressed Rule 404(b) but it did not request a ruling on any evidentiary issue, such as the extent to which he could cross-examine Padilla.
Later in the trial, during a break in Padilla's direct testimony, Mr. Corrales's attorney again raised the Rule 404(b) issue. The government had already elicited some information from Padilla concerning his 2007 offense: He had testified that he had pleaded guilty to smuggling drugs after being stopped in April 2007 at a California border stop where a dog detected drugs. The following colloquy took place in chambers:
[Defense Counsel]: I was reviewing the transcript of the Court's order on the motion to dismiss. And before I started cross-examining Mr. Padilla, or Padilla, it's my understanding the Court would permit me to go into the fact of the prior conviction for impeachment purposes, but not for purposes of Rule 404(b) evidence. Thatto me at least, that means I would not be allowed to address sort of the substantive argument or anyany of the facts of the prior case.
THE COURT: We're not going to try the other case.

[Defense Counsel]: That'sthat's my understanding of the Court's ruling, I just wanted to make sure.
THE COURT: That's right, yeah.
[Defense Counsel]: I would re-urge that motion, Your Honor, based on Mr. Padilla's testimony, however, considering his cold feet when he goes across the border. Given the state of the record as of this morning, as opposed to back when we originally argued the motion, I think that the evidence is now especially relevant to impeach the idea that the Defendantthat Mr. Padilla would hesitate to ever do a drug crossing or that his testimony this morning is true. Meaning that he was so scared he could not continue the drug load. I think the fact that he then later on did another *660 load is evidence that that testimony is untrue, and we'd ask to go into that.
THE COURT: Government.
[Prosecutor]: Well, Judge, first of all, the California matter is two years later. Second of all, I'm not through with Mr. Padilla.
THE COURT: Let's go ahead and finish Mr. Padilla.

R., Vol. 2 Part 3 at 402-04 (emphases added). Thus, the court suggested that it would limit the cross-examination of Padilla, but it also indicated that it would await completion of direct examination before finally deciding.
The remainder of the direct examination significantly changed the context. The prosecutor decided to elicit the facts underlying the 2007 offense. Padilla testified that he had been scared during the 2005 incident but not when crossing the border in 2007, because on the latter occasion he had thought that he was not transporting any drugs. He also said (1) that in 2007, to obtain money to pay bills, he had agreed with two others to smuggle drugs into the United States at some future time (which was supposed to be after the trip on which he was stopped and arrested); (2) that he had agreed despite being scared; and (3) that neither Rodriguez nor Mr. Corrales was involved in the 2007 offense.
Upon the completion of direct examination, Mr. Corrales's attorney argued successfully that the prosecution had opened the door for cross-examination beyond what the court had previously permitted. The exchange proceeded as follows:
[Defense Counsel]: I think the door is open now for testimonyor for questions concerning the prior conviction. The Government has explicitly gone into it. My intent is not to ask about every last circumstance, it's only to ask about what happened that day and then what happened in the subsequent court proceedings. Obviously he had to go to court and plead guilty. He had to affirm his guilt on the record. And what he's saying now is that he wasn't telling the truth when he was in court before. So the Government has elicited testimony regarding this matter, so I'd ask to be able to go into that.
THE COURT: Counsel.
[Prosecutor]: Judge, the direct was the direct was very narrow and did not open the door as counsel is suggesting. It was merely for the purpose of showing [Rodriguez] and the Defendant were not involved in '07 and the reason why the Defendant two years later would get involved. It does not open the door to all the facts underlying the matter in 2007 in California.
THE COURT: Well, I'll let counsel for the Defendant go into those areas that have been directon direct-examination, yes.
Id. at 413-14. Mr. Corrales's attorney did not request further clarification.
Presently, counsel cross-examined Padilla on the 2007 offense:
Q. [Defense Counsel]: In 2007 you decided to drive another load across the border; is that right?
A. No.
Q. Did you ever at any point make an agreement to drive another load of drugs across the border?
A. I was going to intend it.
Q. Tell mewhen you say you were going to intend it, I'm not sure what that means. Can you explain it?
A. He made me an offer to cross drugs into the United States. I told him that I was going to think about it once I did what I had to do. And then probablypossibly I was going to try it or intend it.

*661 Q. What do you mean what you had to do?
A. I had plans to return to Nogales, Mexico toto retrieve a truck that I had flipped over.
Q. Is that what you hadwhat you meant when you said that's what you had to do?
A. Yes.
Q. Okay. Now, you were stopped at the border withon April 21st of 2007. Right?
[exchange with interpreter omitted]
A. Correct.
Q. [Defense Counsel]: Okay. Get us from a truck broke down in Nogales to the border stop.
[Prosecutor]: Judge, we'll object. That's irrelevant, the specific particulars of that event.
THE COURT: Sustained. Move on, please.
Q. [Defense Counsel]: When you're stopped April 21st of 2007, you're stopped with about 18 kilograms of powder cocaine; is that right?
A. That's what they told me.
Q. You didn't know there was any drugs in the car?
A. There should not have been any drugs in the car that day.
Q. Okay. Border agents asked you questions that day?
A. Correct.
Q. Were you extremely nervous the whole time they were asking you those questions?
A. I felt relaxed.
Q. And what were you driving that day?
A. What was I driving?
Q. Yes, sir.
A. Ford pickup, 1999.
Q. Okay. And there was drugs in that pickup. Right?
A. That's what they said they found.
Q. But your testimony is that you didn't know those drugs were there?
A. Correct.
Q. But you pled guilty to the possession of those drugs?
A. I had to do it.
Q. Well, you pled guilty to knowingly possessing those drugs?
A. I had to do it.
Q. And you admitted your guilty in court to knowingly possessing those drugs?
A. I had to do it also.
Q. So what you told the Court that day wasn't true?
A. Correct.
Q. Why did you have to do it?
A. I was going to go to trial.
[Prosecutor]: Judge, we'll object to this. This is irrelevant and immaterial.
THE COURT: Overruled. You may answer.
[exchange with interpreter omitted]
A. They told me that I was going to lose the trial, 100 percent sure, if I didn't do it one day before.
Q. [Defense Counsel]: So you went to court and you told the judge that you knew the drugs were in the car?
A. With my head down.
Q. And was that so you would reduce the amount of time you would spend in prison?
A. Correct.
Q. Okay. It was explained to you probably sometime last week thatactually let me back up. I'm going to *662 ask you a couple of questions. I do not want you to tell me what your attorney told you in response to these questions.
A. Okay.
Q. It was explained to you that I wanted to speak with you about this case.
[Prosecutor]: Judge, we'll object. This is irrelevant and immaterial.
THE COURT: Overruled.
[exchange with interpreter omitted]
A. Correct.
Q. [Defense Counsel]: And that I wanted to ask you questions about what you told the Government here?
A. I couldn't tell you.
Q. Okay. But you're aware I don't have any power to reduce your sentence?
A. I could not correspond. Could not know to correspond. I cannot give a response to that answer.
Q. There's nothing I can do for you as Mr. Corrales' attorney. Right?
[Prosecutor]: Objection, argumentative.
THE COURT: Sustained.
Q. [Defense Counsel]: You refused to discuss the case with us. Right?
A. Correct.
Id. at 436-41 (emphases added).
We discern no limitations on the cross-examination of Padilla regarding his 2007 offense. Only two government objections were sustained; and Mr. Corrales does not (and could not) argue that these two rulings impaired his cross-examination.
Perhaps Mr. Corrales is arguing that he refrained from asking certain questions because of his understanding of the district court's earlier comments. But his brief on appeal does not tell us what additional questions he would have asked, much less what Padilla would have answered. We can hardly determine whether Mr. Corrales was prejudiced without knowing what evidence would have been elicited. See United States v. Adams, 271 F.3d 1236, 1241 (10th Cir.2001) (proffer of evidence is required to preserve claim that trial court improperly excluded testimony). Rather than pointing to excluded evidence, he essentially argues that Padilla's 2007 offense implies Mr. Corrales's own innocence, an argument that could have been (and largely was) made to the jury in closing argument.
At oral argument in this court, Mr. Corrales's attorney was asked what evidence had been excluded. He said that he had been precluded from cross-examining Padilla on several matters: (1) Padilla's demeanor when he was stopped at the border in 2007 (apparently to elicit that he was not nervous when he crossed the border, suggesting that he was an experienced smuggler); (2) the similarity in the amount of cocaine discovered, and how it was hidden, on both occasions; (3) his lying at the time of the 2007 arrest; and (4) his being a high-ranking drug dealer (who likely duped Mr. Corrales into transporting drugs). But Padilla was cross-examined on most of these matters, andparticularly in light of what was allowed during cross-examinationit would have been unreasonable for Mr. Corrales's attorney to believe that he could not have asked Padilla about the secret compartment used in 2007 or his rank in a drug organization.
In short, Mr. Corrales was not deprived of his constitutional right to cross-examine Padilla.

III. CONCLUSION
We AFFIRM Mr. Corrales's convictions.
