ORDER AND JUDGMENT *
Alvaro Chairez-Perez petitions for review of a Board of Immigration Appeals (BIA) order. The BIA dismissed his appeal from the immigration judge’s (IJ) decision denying his request for cancellation of removal. We have jurisdiction under 8 U.S.C. § 1252 and deny the petition.
BACKGROUND
Mr. Chairez-Perez is a native and citizen of Mexico. He entered the United States illegally in 1992. He and his wife have two United States citizen children. In 2008, the Department of Homeland Security initiated removal proceedings against Mr. Chairez-Perez. He conceded removability, but applied for cancellation of removal based on exceptional and extremely unusual hardship to his United States citizen children.
The IJ held a hearing on the cancellation-of-removal request. During the hearing, Mr. Chairez-Perez’s son, Jorge Chai-rez, began testifying about conditions in Mexico. The IJ questioned the relevance of this testimony, noting that Mr. Chairez-Perez’s application indicated the children would not return to Mexico if he were removed. His counsel responded that they wished to present their case in the alternative, detailing the hardship that would occur both if the children remained in the United States and if they left with their father for Mexico. The IJ denied counsel’s request to present an alternative case, ordering him to “move onto a different area.” Admin. R. at 189.
The IJ denied the application for cancellation of removal. He found Mr. Chairez-Perez had failed to establish two of the requisite elements: good moral character, and exceptional and extremely unusual hardship to his citizen children. 8 U.S.C. § 1229b(b)(l)(B), (D).
Mr. Chairez-Perez appealed to the BIA. He argued, among other things, the IJ had “erred in not allowing all relevant and cogent evidence to establish extreme and unusual hardship.” Admin. R. at 465. The BIA remanded to the IJ “so that testimony can be presented on [Mr. Chai-rez-Perez’s] alternative theory of exceptional and extremely unusual hardship[.]” Id. at 457. The BIA instructed that “[o]n remand, both parties may present additional evidence relevant to the respondent’s claim.” Id.
On remand, the IJ said the BIA had remanded solely to permit Mr. Chairez-Perez to present additional evidence on his alternative hardship theory. Mr. Chairez-Perez disagreed, contending the BIA had granted him “a new trial ... on all claims, [at which to] present our evidence.” Id. at 240. In particular, he wished to present additional, updated evidence concerning his good moral character. The IJ rejected this argument and denied Mr. Chairez-Perez’s request to make an offer of proof on good moral character. Mr. Chairez-Perez and his citizen children then testified concerning the hardship they would *781suffer if all of them left the United States for Mexico.
In his subsequent oral decision, the IJ incorporated by reference his previous determination concerning Mr. Chairez-Per-ez’s lack of good moral character. On the hardship issue, he found that Mr. Chairez-Perez had “failed to establish that if he were removed from the United States, and his children ... were to accompany him to Mexico, that they would be subject to exceptional and extremely unusual hardship.” Admin. R. at 115. He therefore again denied Mr. Chairez-Perez’s application on the hardship and moral character grounds.
But in his decision, the IJ also presented an alternate reason for denying relief:
In the event that the United States Board of Immigration Appeals or the 10th Circuit Court of Appeals on review were to find that the Court’s analysis of the hardship question was in error, the Court would note as an alternative finding, that the respondent’s application would also be denied in the exercise of discretion. Pursuant to the REAL ID Act of 2005, a respondent seeking a grant of non-LPR cancellation must establish that he is deserving of a favorable exercise of this Court’s discretion.
Id. at 115-16 (emphasis added).
In support of his discretionary decision, the IJ noted evidence showing that Mr. Chairez-Perez:
• Had been working in the United States illegally and without authorization since 1992;
• Purchased a false lawful permanent resident card in the United States, and used the card to gain employment;
• Claimed, on more than one occasion, to be a lawful permanent resident of the United States to seek employment in this country;
• Had purchased, four or five times, false Social Security cards, and had purchased, four or five times, false Social Security numbers;
• Used false Social Security numbers even after he lawfully obtained a taxpayer identification number;
• Paid a smuggler to bring him to the United States, and later paid a smuggler to bring his family here;
• Failed to register for the draft, as required by the Selective Service Act; and
• Had two convictions for driving under the influence of alcohol.
The IJ concluded that “even if the respondent had established the hardship requirement [he] would deny the application in the exercise of discretion for the reasons set forth above.” Id. at 117.
Mr. Chairez-Perez appealed to the BIA. His appeal brief addressed the scope of the hearing on remand and the IJ’s denial of relief on hardship and good moral character grounds. But he did not specifically challenge the alternative disposition denying him relief in the exercise of discretion.
The BIA dismissed the appeal. It noted Mr. Chairez-Perez’s complaints about the scope of the hearing on remand, but found it “unnecessary to consider whether the Immigration Judge should have reconsidered his previous findings regarding the respondent’s good moral character” and unnecessary to address the IJ’s decision concerning hardship. Id. at 4 & n. 1. Instead, the BIA relied on the IJ’s alternative decision denying the application in his discretion, which it found adequately supported. It noted Mr. Chairez-Perez did not dispute the IJ’s factual findings in support of his discretionary decision. The BIA summarized the factual findings in favor of that decision and concluded “[t]he respondent does not address the [IJ’s] dis*782cretionary denial on appeal. Under these circumstances, we find no reason to disturb the [IJ’s] decision in this case.” Id. at 4.
ANALYSIS
Our scope of review is narrow. The BIA reached its challenged decision on discretionary grounds. We lack jurisdiction to review the discretionary aspects of the agency’s decision to deny an application for cancellation of removal. See 8 U.S.C. § 1252(a)(2)(B)(I) (“[N]o court shall have jurisdiction to review ... any judgment regarding the granting of relief under section ... 1229b”); Sabido Valdivia v. Gonzales, 423 F.3d 1144, 1148-49 (10th Cir.2005) (holding that § 1252(a)(2)(B)(I) strips this court of jurisdiction to review discretionary aspects of a decision concerning cancellation of removal). We may, however, address substantial constitutional claims or questions of law pertaining to the denial of the application, 8 U.S.C. § 1252(a)(2)(D); Alvarez-Delmuro v. Ashcroft, 360 F.3d 1254, 1256 (10th Cir.2004). Our review of such constitutional and legal issues is de novo. Alzainati v. Holder, 568 F.3d 844, 851 (10th Cir.2009).
Mr. Chairez-Perez attempts to raise a constitutional due process issue. He argues the IJ and the BIA could not have decided his application on discretionary grounds because they lacked an adequate factual basis. He contends the IJ did not permit him to present evidence on remand concerning his moral character, thereby depriving him of a full and fair hearing and due process of law.
We cannot address the merits of this argument. Though he was aware of the IJ’s alternate, discretionary ground for his decision, in his second appeal to the BIA, Mr. Chairez-Perez raised no objection to that alternate ground at all. See Appeal Br., Admin. R. at 15-35; Exhibit “A” to Notice of Appeal, id. at 71-72. He only obliquely even mentioned the discretionary component of the cancellation inquiry. See id. at 24 (noting that to receive cancellation of removal, among other things, alien must show he is deserving of a favorable exercise of discretion). His generalized complaints to the BIA about due process and about his not being permitted to present good moral character evidence did not address the discretionary decision.
In sum, Mr. Chairez-Perez failed to exhaust his challenge to the IJ’s discretionary decision before the agency, and we thus lack jurisdiction to consider his challenge to that decision. See, e.g., Sidabutar v. Gonzales, 503 F.3d 1116, 1118 (10th Cir.2007) (“[W]e generally assert jurisdiction only over those arguments that a petitioner properly presents to the BIA”).1 The petition for review is therefore denied.