
557 F.3d 836 (2009)
Anwer M. GHANI and Shabbir Anwer, Petitioners,
v.
Eric H. HOLDER, Jr., Attorney General of the United States, Respondent.
No. 06-3449.
United States Court of Appeals, Seventh Circuit.
Submitted January 24, 2008.
Decided March 9, 2009.
*837 Raymond J. Sanders, Immigrant Law Center, Mahendra R. Mehta, Chicago, IL, for Petitioners.
Siu Ping Wong, Department of Justice, Civil Division, Immmigration Litigation, Washington, DC, for Respondent.
Before POSNER, RIPPLE and TINDER, Circuit Judges.
RIPPLE, Circuit Judge.
Anwer M. Ghani and his son, Shabbir Anwer, were issued separate notices to appear in immigration court to face charges of removability.[1] An immigration judge determined that both men were subject to removal because they had overstayed their visas. The immigration judge also found that neither of the men was eligible for cancellation of removal and, therefore, entered orders of removal. Mr. Ghani's application for voluntary departure was denied; Mr. Anwer's application was granted. The Board of Immigration Appeals affirmed the immigration judge's decisions without opinion. Mr. Ghani and Mr. Anwer timely petitioned this court for review. For the reasons explained below, we deny their petitions.

I

BACKGROUND

A.
Anwer M. Ghani and his now-adult son, Shabbir Anwer, are natives and citizens of Pakistan. On October 5, 1991, they were admitted to the United States as non-immigrant visitors with permission to remain until April 4, 1992. They overstayed their visitor visas and, on February 13, 2003, they were issued separate notices to appear in immigration court to face charges of removability. Mr. Ghani was released on a $5000 bond; Mr. Anwer was released on his own recognizance.
Mr. Ghani had attempted to enter or to remain unlawfully in the United States on two previous occasions. On October 1, 1978, Mr. Ghani entered the United States on a non-immigrant visa. He overstayed that visa; after he was apprehended, he *838 departed on August 20, 1984, on a grant of voluntary departure.
On March 3, 1988, Mr. Ghani was caught attempting to enter the United States at Seattle International Airport using an altered passport bearing the name "Abdul Ghaffar." He pleaded guilty to making a false statement in violation of 18 U.S.C. § 1001. He was ordered removed to Pakistan on April 29, 1988. Mr. Ghani did not disclose this conviction when he re-entered the United States in 1991.

B.
The removal proceedings in the present case began on April 11, 2003. Before the immigration judge ("IJ"), Mr. Ghani conceded the first four of the seven factual allegations against him: that he is not a native and citizen of the United States; that he is a native and citizen of Pakistan; that he was admitted to the United States on October 5, 1991, as a non-immigrant visitor; and that he overstayed his visa without INS authorization. Mr. Ghani denied the last three allegations: that he previously was ordered removed in 1988; that he was removed or that he departed pursuant to that order on April 29, 1988; and that he was convicted of making false statements under 18 U.S.C. § 1001. Mr. Ghani also admitted the Government's first charge of removability: that he overstayed his visa. He denied the Government's other two charges: that he previously had been removed and that he was convicted of a crime involving moral turpitude. Mr. Anwer admitted that he was subject to removal because he had overstayed his visa. Both men also indicated to the IJ that they would seek relief in the form of cancellation of removal under section 240A(b) of the Immigration and Nationality Act ("INA"), 8 U.S.C. § 1229b(b), with Mr. Anwer's eligibility for relief contingent upon a grant of relief to Mr. Ghani.
The IJ determined that the first charge against Mr. Ghani, based on the overstayed visa, had been proved by clear and convincing evidence. The judge did not sustain the second charge, based on Mr. Ghani's previous removal, because that removal was the result of exclusion proceedings rather than removal proceedings. The IJ concluded that the third charge, based upon Mr. Ghani's previous conviction, could not be sustained because Mr. Ghani already had been deported for that conviction.
The IJ further determined that Mr. Ghani was not eligible to apply for cancellation of removal under INA section 240A(b), 8 U.S.C. § 1229b(b), because his conviction for making false statements in violation of 18 U.S.C. § 1001 was for a crime involving moral turpitude.[2] The IJ also denied Mr. Ghani's request for voluntary departure because he found that Mr. Ghani had "disregarded the immigration laws of the United States." A.R. 37. The IJ based this finding on two grounds: (1) Mr. Ghani's failure to mention, in his most recent application for a B-1 visa, that he had been convicted of an offense; and (2) Mr. Ghani's repeated attempts to enter or to remain illegally in the United States.
Regarding Mr. Anwer, the IJ found that the charge against him had been proved by clear and convincing evidence. The IJ denied his application for cancellation of removal because he had no "qualifying relative" under INA section 240A(b)(1)(D), 8 *839 U.S.C. § 1229b(b)(1)(D). The IJ did, however, grant Mr. Anwer's petition for voluntary departure.
Both men timely appealed the IJ's decision. On August 15, 2006, the Board of Immigration Appeals ("BIA") affirmed the IJ's decision without opinion. Mr. Ghani and Mr. Anwer then filed a petition for review with this court.

II

DISCUSSION
Mr. Ghani attacks the IJ's decision on nearly a dozen grounds. Most of these are simply different formulations of a single contention: that the IJ erred in considering Mr. Ghani's section 1001 conviction because that conviction was constitutionally infirm. Mr. Ghani contends that the charge brought against him for violating section 1001a charge to which he pleaded guilty in 1988was brought without indictment and that, therefore, the conviction cannot bar his application for cancellation of removal.
As a threshold matter, we note that Mr. Ghani did not raise this claim before the BIA; therefore, the issue is waived. See Hamdan v. Gonzales, 425 F.3d 1051, 1058 n. 14 (7th Cir.2005) (arguments not raised to the BIA are waived for failure to exhaust administrative remedies).
Mr. Ghani now argues that the waiver should be excused because his previous counsel rendered ineffective assistance by failing to raise the alleged lack of an indictment. His counsel's failure to raise the lack of indictment did not render his assistance ineffective, however, because "an alien may not collaterally attack a conviction in an INS proceeding." Mansoori v. INS, 32 F.3d 1020, 1024 (7th Cir. 1994) (citing Palmer v. INS, 4 F.3d 482, 489 (7th Cir.1993); Guillen-Garcia v. INS, 999 F.2d 199, 204 (7th Cir.1993); and Rassano v. INS, 377 F.2d 971, 974 (7th Cir. 1966)). Furthermore, Mr. Ghani pleaded guilty to the charge of violating section 1001. In doing so, he waived the right to challenge the validity of his conviction based on a claim of constitutional irregularity that occurred prior to the plea. See Tollett v. Henderson, 411 U.S. 258, 267, 93 S.Ct. 1602, 36 L.Ed.2d 235 (1973) ("When a criminal defendant has solemnly admitted in open court that he is in fact guilty of the offense with which he is charged, he may not thereafter raise independent claims relating to the deprivation of constitutional rights that occurred prior to the entry of the guilty plea."). After pleading guilty, a criminal defendant may challenge his conviction only on the basis that his plea was not "voluntary and intelligent." Id.
Mr. Ghani further argues that his guilty plea was not voluntary and intelligent because his counsel in his criminal case also was ineffective. As we have just explained, however, immigration proceedings are not a permissible venue for attacking the validity of a criminal conviction. We therefore cannot accept Mr. Ghani's argument that his section 1001 conviction was invalid.
Mr. Ghani also submits that the record does not support the IJ's finding that he had been convicted of violating section 1001. Mr. Ghani failed to raise this argument before the IJ or the BIA, and therefore it is waived as well. See Hamdan, 425 F.3d at 1058 n. 14. In any event, the argument is without merit. The IJ based his finding on the order of conviction entered by the district court on April 20, 1988, which expressly states that Mr. Ghani had pleaded guilty to violating 18 U.S.C. § 1001. The IJ was entitled to rely on the order of conviction, because the INA provides that an "official record of judgment and conviction" "shall constitute *840 proof of a criminal conviction." 8 U.S.C. § 1229a(c)(3)(B).
Mr. Ghani further contends that, even if the evidence supports the IJ's finding that he was convicted of violating section 1001, it does not support the finding that the violation was a crime involving moral turpitude. This claim is also waived because Mr. Ghani failed to raise it before the BIA. Even if Mr. Ghani's failure to exhaust were to be excused, however, this argument would fail on the merits as well.
The INA does not define the term "crime involving moral turpitude." Administrative agencies' interpretations of ambiguous statutory provisions generally are entitled to deference. Chevron U.S.A., Inc. v. Natural Res. Def. Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). Indeed, we recently held that the BIA's interpretation of the term "crime involving moral turpitude" is entitled to Chevron deference. Ali v. Mukasey, 521 F.3d 737, 739 (7th Cir.2008). We have questioned, however, whether Chevron deference is appropriate in cases where the BIA affirms without opinion under the "streamlined" procedure set forth in 8 C.F.R. § 1003.1(e)(4), as it did in this case, because streamlined affirmances under section 1003.1(e)(4) approve the result reached by the IJ, but not necessarily the IJ's reasoning, and the BIA does not provide any reasoning of its own. See Gutnik v. Gonzales, 469 F.3d 683, 689-90 (7th Cir.2006). Thus, although Chevron requires us to defer to a "plausible `agency answer'" as to the proper interpretation of an ambiguous term, it is questionable at best whether a streamlined affirmance can be said to be a definitive pronouncement of the BIA's position because IJ decisions that have been affirmed via section 1003.1(e)(4) do not act as binding precedent on the BIA or other IJs. Id. As the Third Circuit has noted, "deferring to the reasoning of an IJ from which the BIA would be free to depart in other cases would seem highly problematic." Id. (quoting Smriko v. Ashcroft, 387 F.3d 279, 289 n. 6 (3d Cir.2004)).
We need not resolve that issue today, however, because it has no bearing on the outcome of this case. There can be no question that a violation of section 1001 is a crime involving moral turpitude. Section 1001 reads as follows:
(a) Except as otherwise provided in this section, whoever, in any matter within the jurisdiction of the executive, legislative, or judicial branch of the Government of the United States, knowingly and willfully
(1) falsifies, conceals, or covers up by any trick, scheme, or device a material fact;
(2) makes any materially false, fictitious, or fraudulent statement or representation; or
(3) makes or uses any false writing or document knowing the same to contain any materially false, fictitious, or fraudulent statement or entry;
shall be fined under this title [or] imprisoned not more than 5 years. . . .
18 U.S.C. § 1001. As we have recognized in the past, "it is settled that `crimes in which fraud [is] an ingredient' involve moral turpitude." Padilla v. Gonzales, 397 F.3d 1016, 1020 (7th Cir.2005) (alteration in original) (quoting Jordan v. De George, 341 U.S. 223, 232, 71 S.Ct. 703, 95 L.Ed. 886 (1951)). Even if the conduct for which Mr. Ghani was convicted did not rise to the level of fraud, however, his conviction necessarily establishes that he "knowingly and willfully" lied to the Government of the United States about a material matter. As we recognized in Padilla, "almost all courts have held that `intentionally deceiving the government involves moral turpitude.'" *841 Id. (quoting Omagah v. Ashcroft, 288 F.3d 254, 262 (5th Cir.2002)). Moreover, nearly every court to consider the issue has concluded that crimes involving willful false statements are turpitudinous.[3] Accordingly, we conclude that a violation of 18 U.S.C. § 1001 is a crime involving moral turpitude as that term is used in the INA.
Mr. Ghani presents two other arguments, both of which are waived for failure to exhaust them before the BIA, and both of which lack merit in any event. He submits that the IJ failed to advise him of his right to possible relief under the amnesty provisions in section 201(a) of the Immigration Reform and Control Act of 1986 ("IRCA"), 8 U.S.C. § 1255a. Mr. Ghani was not eligible for amnesty under IRCA, however, because the application period for amnesty expired on May 4, 1988, 8 C.F.R. § 245a.2(a)(1) (1988), and because he had been convicted of a felony. See 8 U.S.C. § 1255a(a)(4)(B) (stating that the alien must establish that he "has not been convicted of any felony or of three or more misdemeanors committed in the United States").
Finally, Mr. Ghani submits that the IJ erred in applying the "stop-time rule" retroactively to his section 1001 conviction. The stop-time rule applies to the continuous-physical-presence requirement set forth in section 240A(b)(1)(A) of the INA, 8 U.S.C. § 1229b(b)(1)(A), but the IJ did not base his denial of cancellation of removal on a finding that Mr. Ghani did not meet this requirement. Rather, the denial was based on section 240A(b)(1)(C), 8 U.S.C. § 1229b(b)(1)(C), which provides that conviction for a crime involving moral turpitude renders an alien ineligible for cancellation of removal. The stop-time rule is irrelevant in this case.
We therefore deny Mr. Ghani's petition for review of the BIA's decision. Mr. Anwer's petition for review also must be denied because his only basis for cancellation of removal was Mr. Ghani's presence in the United States as a qualifying relative under section 240A(b)(1)(D) of the INA, 8 U.S.C. § 1229b(b)(1)(D).[4]

Conclusion
For the reasons set forth in this opinion, the petition for review is denied.
PETITION FOR REVIEW DENIED.
NOTES
[1]  Mr. Ghani was charged under 8 U.S.C. §§ 1227(a)(1)(B), 1227(a)(1)(A) and 1227(a)(2)(A)(I). Mr. Anwer was charged under 8 U.S.C. § 1227(a)(1)(B).
[2]  The IJ rejected Mr. Ghani's argument that, because he was in an INA section 237 proceeding, the only types of criminal acts that precluded him from eligibility for cancellation of removal were those described in INA section 237(a)(2) or 237(a)(3). Mr. Ghani challenged this aspect of the IJ's decision in his appeal to the BIA, but has not renewed that challenge in his petition to this court.
[3]  See, e.g., Padilla v. Gonzales, 397 F.3d 1016, 1019-21 (7th Cir.2005) (holding that obstruction of justice is a crime involving moral turpitude and noting that "[c]rimes that do not involve fraud, but that include dishonesty or lying as an essential element also tend to involve moral turpitude" (citation and quotation marks omitted)); Itani v. Ashcroft, 298 F.3d 1213, 1216 (11th Cir.2002) (holding that misprision of a felony is a crime involving moral turpitude and noting generally that "a crime involving dishonesty or false statement is considered to be one involving moral turpitude" (citation and quotation marks omitted)); Kabongo v. INS, 837 F.2d 753, 758 (6th Cir. 1988) (holding that a conviction for violating section 1001 "may be considered as involving moral turpitude for purposes of denying voluntary departure"). Cf. Orlando v. Robinson, 262 F.2d 850, 851 (7th Cir. 1959) ("At the risk of being labeled prosaic we do not classify a prevaricator as a person of good moral character. Certainly mendacity is not a virtue.").
[4]  Section 240A(b)(1)(D) provides that removal may be cancelled if the alien "establishes that removal would result in exceptional and extremely unusual hardship to the alien's spouse, parent, or child, who is a citizen of the United States or an alien lawfully admitted for permanent residence." 8 U.S.C. § 1229b(b)(1)(D).
