GORSUCH, Circuit Judge.

At a bar in Palomas, Mexico, Alfredo Hernandez-Hernandez, a Mexican citizen twice deported from the United States, consumed a sufficient amount of alcohol and marijuana to blackout. The next thing he knew, Mr. Hernandez was in the United States without any recollection how he got there and, in short order, arrested for illegally reentering the country. Today, we are asked to decide whether the district court’s decision to exclude from trial evidence of Mr. Hernandez’s intoxication and resulting amnesia violated his constitutional right to present a defense. We hold that it did not, and so affirm the district court’s judgment.

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According to Mr. Hernandez, he consumed more than a fifth of a quart of liquor, as well as some marijuana, at a bar in Palomas and promptly blacked out. When Mr. Hernandez regained his faculties, he found himself in the United States and confronted by a United States Border Patrol Agent. In response to the agent’s questions, Mr. Hernandez admitted that he was a Mexican national and acknowledged that he had no documentation allowing him to be legally present in the United States.

Mr. Hernandez was taken to a Border Patrol Station in Columbus, New Mexico, where an agent ran Mr. Hernandez’s name through a law enforcement database. This background check revealed a somewhat lengthy criminal history — including convictions stemming from various fights Mr. Hernandez engaged in while intoxicated. As a result of these convictions, Mr. Hernandez already had been twice deported from the United States.

Rather than simply deporting him again, this time authorities indicted Mr. Hernandez for violation of 8 U.S.C. § 1326(a) and (b), and, more specifically, under the provision making it unlawful to be “found in” the United States illegally after a prior deportation. 1 In pre-trial proceedings, the *1238 government filed a motion in limine, seeking to exclude from trial any evidence that Mr. Hernandez might present regarding his voluntary intoxication. 2 Mr. Hernandez opposed the government’s motion, arguing that he should be allowed to show that “he has absolutely no memory of taking any actions to illegally cross the border” and “does not know whether his subsequent presence in the United States was voluntary and knowingly made. If [he] was brought to the United States and dumped on the United States side while he was passed out, clearly such an act would be a viable and acceptable defense to the crime charged.” Defendant’s Opp. to the Govt’s Motion In Limine at 2. In aid of this argument, Mr. Hernandez proffered not just his own testimony but also offered Dr. Orrin McCleod, who sought to testify that Mr. Hernandez’s history of alcoholism caused him to suffer “intoxicant amnesia” from the consumption of large amounts of alcohol, and Eugenio Vergara-Sosa, a fellow detainee who was prepared to testify that Mr. Hernandez was highly intoxicated and disoriented the day of his arrest.

The district court granted the government’s motion and excluded Mr. Hernandez’s proffered evidence. The court reasoned that Section 1326 creates only a “general intent” crime, that as a rule voluntary intoxication is not a defense to such crimes, and that Mr. Hernandez’s evidence amounted to little more than an effort to effect an end-run around this rule. Following the district court’s ruling, Mr. Hernandez entered a conditional plea of guilty, reserving his right to challenge the district court’s evidentiary ruling, and was sentenced to 21 months imprisonment.

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On appeal, Mr. Hernandez argues that the district court’s refusal to entertain evidence about his blackout violated his Fifth Amendment right to due process and his Sixth Amendment right to compulsory process. The right to defend oneself in a criminal trial by presenting witnesses and other forms of evidence is, of course, a keystone of our legal system. See, e.g., Washington v. Texas, 388 U.S. 14, 18-19, 87 S.Ct. 1920, 18 L.Ed.2d 1019 (1967); Roviaro v. United States, 353 U.S. 53, 77 S.Ct. 623, 1 L.Ed.2d 639 (1957). But we have held that this right, while fundamental, is “not absolute,” and surely a defendant cannot present testimony willy nilly that has nothing to do with the crime charged. United States v. Bautista, 145 F.3d 1140, 1151-52 (10th Cir.1998). Accordingly, we have held that the district court enjoys substantial discretion in deciding whether to receive or exclude evidence at trial. Id. And when it comes to assessing whether the constitutionally protected right to call witnesses and produce evidence has been trenched upon, we have indicated that we will reverse a district court’s decision excluding evidence if, but *1239 only if, the proffered evidence is both relevant and material (that is, of such an exculpatory nature that its exclusion can be said to affect a trial’s outcome). Richmond v. Embry, 122 F.3d 866, 872 (10th Cir.1997); see also United States v. Dowlin, 408 F.3d 647, 659 (10th Cir.2005). In this case, we believe Mr. Hernandez’s evidence fails at the first step because he has not established its relevance.

Mr. Hernandez, of course, contests this, suggesting his proffered proof bears on the mens rea element of the crime. But the mens rea required to secure a Section 1326 conviction for being unlawfully “found in” the United States is limited. In the past, we admit, the mental elements associated with Section 1326 were sometimes shrouded by reference to vague concepts like “general” and “specific” intent. See, e.g., United States v. Martinez-Morel, 118 F.3d 710, 716 (10th Cir.1997); United States v. Miranda-Enriquez, 842 F.2d 1211, 1212 (10th Cir.1988); United States v. Hernandez, 693 F.2d 996, 1000 (10th Cir.1982). But in this area, as in many others, see, e.g., United States v. Zunie, 444 F.3d 1230, 1233-35 (10th Cir.2006); United States v. Teague, 443 F.3d 1310, 1319 (10th Cir.2006), we have sought to follow the thrust of modern American jurisprudence and clarify the required mens rea, often by reference to the Model Penal Code’s helpfully defined terms, rather than persist in employing opaque common law labels that sometimes blur the line between distinct mental elements. 3

Accordingly, fully twenty years ago, we announced that the only mens rea required to establish a violation under Section 1326’s provision prohibiting those previously denied the right to be in the United States from “entering]” the country is a showing “that the defendant’s acts were intentional. No intent to break the law— whether characterized as ‘specific intent’ or ‘general criminal intent’ — must be proved.” Mirandar-Enriquez, 842 F.2d at 1212. A decade later, in Martinez-Morel, we added that this same intent — “the intent to do the act of entering the country” — will suffice to support a conviction under Section 1326’s provision, now before us, making it unlawful to be “found in” the United States after a prior deportation. 118 F.3d at 713, 717; see also United States v. Meraz-Valeta, 26 F.3d 992, 997 (10th Cir.1994) (noting that the actus reus for a prosecution under Section 1326’s “found in” language is “returning] to the United States without the permission of the Attorney General”), overruled on other grounds by United States v. Aguirre-Tello, 353 F.3d 1199 (10th Cir.2004). 4

*1240 Simply put, we have recognized that laws pertaining to border control are matters over which Congress holds plenary power, are generally subjected by Congress “to stringent public regulation,” Martinez-Morel, 118 F.3d at 716 (quoting United States v. X-Citement Video, Inc., 513 U.S. 64, 71, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994)), and are often treated as nearly (though not quite, given that a mens rea element is required) matters of “strict liability,” id. As the Supreme Court has instructed, “[ujnder such [regulatory] statutes we have not required that the defendant know the facts that make his conduct fit the definition of the offense.” Staples v. United States, 511 U.S. 600, 607 n. 3, 114 S.Ct. 1793, 128 L.Ed.2d 608 (1994). 5

For his part, Mr. Hernandez, although contending that his intoxication has a relationship to the necessary mens rea, does not argue that his alcohol- and drug-induced blackout is sufficient to negate the limited mens rea required by the statute. To the contrary, he “has maintained since this issue has arisen that the Government is correct that voluntary intoxication is not a defense to this crime,” Opening Br. at 13, and that voluntary intoxication provides a defense only when “specific” intent — or, a bit more precisely, an intent to do something more than just the physical act the crime requires — is necessary. See United States v. Hatatley, 130 F.3d 1399, 1405 (10th Cir.1997) (intoxication not a defense to “general intent” crimes); United States v. Sands, 968 F.2d 1058, 1064 (10th Cir.1992) (same); see also United States v. Blair, 54 F.3d 639, 642 (10th Cir.1995) (distinguishing general and specific intent). 6

Instead, while the mens rea required under Section 1326 is limited, Mr. Hernandez emphasizes that, under the theory the government pursued in this case, it does require at least an intent to undertake the physical act that results in the defendant crossing the border. And Mr. Hernandez argues that, because of his blackout, there is a “complete vacuum in his memory,” Opening Br. at 17, so that it is possible he was abducted and did not enter the United States of his own volition. Toward this end, Mr. Hernandez highlights our case law holding that “if appellant was drugged and carried across the line, he would not *1241 be guilty of the” mens rea required by Section 1326. Miranda-Enriquez, 842 F.2d at 1212 (internal quotation marks and citations omitted).

In approaching this argument, we agree with our sister circuits that an alien’s presence in the United States gives rise to a natural, common sense inference that his or her presence was intentional in the very limited, Section 1326 sense. After all, those crossing the border usually do so intending their own physical actions. See United States v. Quintana-Torres, 235 F.3d 1197, 1200 (9th Cir.2000); see also United States v. Rivera-Sillas, 417 F.3d 1014, 1020 (9th Cir.2005) (“We are comfortable presuming that a defendant who is found in the United States willfully and knowingly acted in order to enter this country.”). Still, this inference can be overcome; while most border crossings are surely intentional in the Section 1326 sense, neither can we deny that the trafficking of human beings against their will across international boundaries is a reality. 7 But, “[t]o dispel the inference, the alien would have to demonstrate that one of the speculative possibilities of involuntary entry had actually taken place.” Quintana-Torres, 235 F.3d at 1200. And our test for assessing the relevance of evidence seeking to dispel this inference, as always, turns on whether the proffered proof makes a “fact that is of consequence to the determination of the action more probable or less probable.” Fed.R.Evid. 401.

So, Mr. Hernandez was surely entitled to produce evidence making it “more probable” that he was taken across the border against his will. The problem is that Mr. Hernandez’s proof in this case does no such thing. An ordinary intoxication defense, where permissible, is relevant only because it makes it less likely the defendant possessed the mental state the government is required to prove. Here, however, Mr. Hernandez does not seek to argue that his intoxication would have negated the requisite mens rea under Section 1326. Instead, he wishes to offer his intoxication as evidence that his lack of memory is credible, and it is his lack of memory, Mr. Hernandez submits, that goes to the requisite mental state. Because he cannot remember anything after he blacked out, Mr. Hernandez seems to suggest, anything is possible. Maybe he was kidnapped. Maybe he was dragged across the border by a drinking pal. Maybe someone was playing a practical joke and transported him in a catatonic state into the United States. The difficulty lies in the fact that Mr. Hernandez’s lack of memory leaves equally open the possibility that he walked across the border under his own steam. Or hitched a ride. Or paid to be driven. Simply put, Mr. Hernandez’s proof does not make it any more or less likely that he was (innocently) carried across the border against his will or (culpably) intended the physical actions that transported him to the United States.

Had Mr. Hernandez’s proffer included any evidence suggesting that he was taken across the border against his will, that would be one thing. But inviting the jury to guess about the mode of Mr. Hernandez’s arrival in the United States based on the absence of proof (a “complete vacuum in his memory”) is another, and the district court properly ruled it out of bounds. Relevant evidence does not include the suggestion of speculative possibilities. See Holmes v. South Carolina, 547 U.S. 319, 327, 126 S.Ct. 1727, 164 L.Ed.2d 503 (2006) *1242 (evidence may be permissibly excluded “where the evidence is speculative or remote, or does not tend to prove or disprove a material fact in issue at the defendant’s trial”) (internal quotation omitted); United States v. Isaac-Sigala, 448 F.3d 1206, 1210 (10th Cir.2006) (“[A] jury will not be allowed to engage in a degree of speculation and conjecture that renders its finding a guess or mere possibility.”) (internal quotations and alterations omitted).

Indeed, we have upheld analogous decisions excluding evidence in Section 1326 prosecutions in the past. In Martinez-Morel, for example, the defendant wished to testify in response to the charge that he was unlawfully found in the United States that he had believed in good faith, albeit erroneously, that he had entered the country legally. The district court refused to entertain the evidence and we affirmed, explaining that it simply “is not relevant to a prosecution for illegal reentry after deportation, and the district court did not abuse its discretion in excluding” it. 118 F.3d at 714; see also Mirandar-Enriquez, 842 F.2d at 1212. Exactly the same might be said here.

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The Fifth and Sixth Amendment right to produce witnesses on one’s behalf, while fundamental, does not extend to irrelevant (or immaterial) matters. The testimony excluded here simply was not relevant to any fact at issue in the defense Mr. Hernandez pursued — making it neither more nor less probably true. Accordingly, the district court’s decision to exclude it was appropriate.

Affirmed.

. 8 U.S.C. 1326(a) provides:

Subject to subsection (b) of this section, any alien who (1) has been denied admission, *1238 excluded, deported, or removed or has departed the United States while an order of exclusion, deportation, or removal is outstanding, and thereafter (2) enters, attempts to enter, or is at any time found in, the United States, unless (A) prior to his reembarkation at a place outside the United States or his application for admission from foreign contiguous territory, the Attorney General has expressly consented to such alien's reapplying for admission; or (B) with respect to an alien previously denied admission and removed, unless such alien shall establish that he was not required to obtain such advance consent under this chapter or any prior Act, shall be fined under Title 18, or imprisoned not more than 2 years, or both.

. On appeal, Mr. Hernandez asserts that the government sought to preclude him from presenting any and all evidence as to the voluntariness of his reentry. Op. Br. at 4. Although that is a fair reading of the motion in limine, the motion was granted only with respect to the defense of voluntary intoxication, R., Vol. IV at 9, and that is the only issue remaining before us.

. See, e.g., Wayne G. Lafave, 1 Substantive Criminal Law § 5.2 (2d ed. 2003) ("The modem view [in the United States] ... is that it is better to draw a distinction between intent (or purpose) on the one hand and knowledge on the other.”); Model Penal Code § 2.02 (distinguishing between intent or purpose and knowledge, recklessness, and negligence); Clark v. Arizona, 548 U.S. 735, 126 S.Ct. 2709, 2729, 165 L.Ed.2d 842 (2006) ("[T]he modern tendency has been toward more specific descriptions” of mens rea); Morissette v. United States, 342 U.S. 246, 250, 72 S.Ct. 240, 96 L.Ed. 288 (1952) (distinguishing between species of mens rea "is no provincial or transient notion. It is as universal and persistent in mature systems of law as belief in freedom of the human will and a consequent ability and duty of the normal individual to choose between good and evil”).

. The government's proposed jury instruction in this matter suggested that it had to prove that the defendant "knowingly was found.” We are unsure what it would mean to be "knowingly found.” The government cites to two cases in support of employing that formulation, United States v. Anaya, 117 F.3d 447, 449 (10th Cir.1997) and Meraz-Valeta, 26 F.3d at 997, neither of which includes such language. The government also cites to the 10th Circuit Pattern Jury Instruction § 2.05 (2005), which appears to use "knowing” to modify the act of being found in the United States. The Pattern Jury Instruction, in turn, indicates that it is based on Marlinez-Morel, *1240 118 F.3d 710. Yet, Martinez-Morel merely quotes the district court's jury instruction in that case; it did not analyze or approve the instruction, and it ultimately held that the mens rea element of the offense can be satisfied by showing that the defendant had "the intent to do the act of entering the country,” id. at 717. Whether there may be some additional way of satisfying the mens rea associated with Section 1326's "found in” provision— such as by simply proving that the defendant knew he or she was physically within the United States — is not before us.

. While we have done much to clarify the issue of the requisite intent under Section 1326, we do not doubt that some issues remain unresolved. For example, in United States v. Gracidas-Ulibarry, 231 F.3d 1188 (9th Cir.2000) (en banc), the Ninth Circuit held that the mens rea in a prosecution under Section 1326 for attempted reentry of a deported alien differed from the mens rea for a completed reentry in that an attempted reentry prosecution requires the government to prove the defendant "had the purpose, i.e., conscious desire, to reenter the United States without the express consent of the Attorney General,” id. at 1196, while the latter does not. But see United States v. Rodriguez, 416 F.3d 123, 125 (2d Cir.2005) (rejecting, and collecting cases rejecting, Gracidas-Ulibarry’s holding as to the mens rea for attempted reentry); see also supra n. 4 (highlighting another mens rea ambiguity). We need not resolve such issues today, however.

. Though some commentators have "suggested eschewing” the "mechanical formulation” that voluntary intoxication can negate only "specific intent” crimes, see United States v. Abeyta, 27 F.3d 470, 474 n. 8 (10th Cir.1994), that issue is not before us today.

. See, e.g., Department of Justice, Report on Activities to Combat Human Trafficking, Fiscal Years 2001-05.