Albert Musollari and his wife, Vergjin-ush, are natives and citizens of Albania who entered the United States in 2001 on visitor’s visas. They overstayed and then sought asylum, withholding of removal, and protection under the Convention Against Torture (“CAT”). An Immigration Judge (“IJ”) denied their application, finding Musollari’s testimony incredible, and the Board of Immigration Appeals (“BIA”) affirmed. Because the decisions by the IJ and the BIA are supported by substantial evidence and the record does not compel a contrary conclusion, we deny the Musollaris’ petitions for review.
I. Background
The Musollaris came to the United States from Albania in January 2001 on visas that permitted them to stay for six months. They have two children: Kevin, who was born in Albania, was left behind and remains there; and David, who was born in the United States. The Musollaris did not return to Albania by their depar*507ture date and subsequently filed an application seeking asylum, withholding of removal, and protection under the CAT.1 The petition was rejected by an asylum officer, and the Musollaris appeared before an IJ for removal proceedings. At the hearing Musollari recounted a history of hardships he said he and his family had suffered as a result of his involvement in Albanian politics. What follows is a summary of his testimony.
Musollari served in the Albanian military during the final days of communist control in the early 1990s. In 1991 Musol-lari disobeyed a direct order from his superior officer to fire on a group of civilians who were attempting to flee the country by boat. Fearing reprisal for his disobedience, Musollari boarded the boat with the civilians; it was bound for Italy. Italian officials, however, returned Musollari and other soldiers to Albania, and upon their return he and the others were arrested and beaten by Albanian officials.
In 1992 the communist government fell and the Democratic Party, of which Musol-lari is a member, took power. That party’s electoral superiority lasted until 1997 when the Socialist Party swept the elections. Musollari, however, claimed that the Socialists seized the reins of power “by force of arms,” through violence and intimidation. He testified that he became a target of these tactics after he gave a speech at a protest rally in his hometown of Korcé. Musollari was forced to flee, and his home was ransacked during his absence. His neighbors told him the police, not random intruders, were the culprits.
Musollari was arrested in October 1997 and again in September 1998. He testified that he was beaten during these detentions and interrogated about his activities in the Democratic Party; he also said the police tried to force him to spy on other members of the party. The police arrested Musol-lari again in November of 2000, after he served as an election observer for the Democratic Party during elections the previous month. He claimed that in the course of his duties as an election observer, he witnessed voting irregularities that enabled the Socialist Party to win the election. He testified that he was again interrogated about the Democratic Party’s activities and threatened with violence against his family.
After this last incident, the Musollaris decided to flee Albania. They obtained nonimmigrant visas permitting them to come to the United States for six months, but were forced to leave their son, Kevin, behind. They arrived in the United States in 2001, overstayed, and sought asylum in 2002.
The Musollaris went before an IJ in the fall of 2003. The IJ denied their claims for asylum, withholding of removal, and protection under the CAT because he found Musollari’s testimony incredible and lacking corroboration. Further, the IJ denied voluntary departure because he believed that Musollari was not of good moral character. The Musollaris appealed, and the BIA affirmed the IJ’s decision except as to voluntary departure. The case was remanded to the IJ on that issue.
At the subsequent hearing before the IJ, the Musollaris withdrew their application for voluntary departure and instead sought to present new evidence on their claims. They did not state what the new evidence *508was, however. So the IJ denied the request and entered an order of removal. The Musollaris again appealed, and the BIA affirmed.
II. Discussion
The BIA adopted the IJ’s opinion, so we base our review on the IJ’s analysis. Bal-ogun v. Ashcroft, 374 F.3d 492, 498 (7th Cir.2004).. Our review of an order denying asylum based on a failure to prove eligibility is extremely deferential; “the administrative findings of fact are conclusive unless any reasonable adjudicator would be compelled to conclude to the contrary.” 8 U.S.C. § 1252(b)(4)(B); Sina v. Gonzales, 476 F.3d 459, 461 (7th Cir.2007); Balogun, 374 F.3d at 498 (holding that the IJ’s findings may be overturned only if “the evidence compels a different result”). If an alien demonstrates eligibility, the Attorney General has discretion to grant or deny asylum. Ghebremedhin v. Ashcroft, 392 F.3d 241, 244 (7th Cir.2004). “[T]he Attorney General’s discretionary judgment whether to grant relief under section 1158(a) of this title shall be conclusive unless manifestly contrary to the law and an abuse of discretion.” 8 U.S.C. § 1252(b)(4)(D).
The IJ’s credibility determinations are also accorded substantial deference and should be overturned only “under extraordinary circumstances.” Gjerazi v. Gonzales, 435 F.3d 800, 807 (7th Cir.2006). Deference is not unlimited, however; the IJ’s rulings cannot be based on “conjecture” or “insufficient or incomplete evidence” and instead “must be supported by specific, cogent reasons” which “bear a legitimate nexus to the finding.” Id.
The Attorney General has discretion to grant asylum to an alien “refugee.” 8 U.S.C. § 1158(b)(1)(A). A “refugee” is one who is unable or unwilling to return to his country of origin “because of persecution or a well-founded fear of persecution on account of race, religion, nationality, membership in a particular social group, or political opinion.” 8 U.S.C. § 1101(a)(42). The applicant has the burden of proving eligibility for asylum, and the applicant’s testimony alone may be sufficient to sustain the burden if the applicant’s testimony is credible. 8 C.F.R. § 208.13(a). Refugee status may be proven in one of two ways. First, “if an applicant proves past persecution, a rebuttable presumption arises that the alien has a well-founded fear of future persecution.” Capric v. Ashcroft, 355 F.3d 1075, 1084 (7th Cir. 2004); 8 C.F.R. § 208.13(b)(1). Second, an applicant may prove a well-founded fear of persecution by demonstrating his “fear is subjectively genuine and objectively reasonable in light of credible evidence.” Capric, 355 F.3d at 1085; 8 C.F.R. § 208.13(b)(2). The subjective component “turns largely upon the applicant’s own testimony and credibility,” Capric, 355 F.3d at 1085, while the objective component requires the applicant to show that he will be singled out for persecution or that a group to which the applicant belongs is subject to a pattern or practice of persecution. 8 C.F.R. § 208.13(b)(2).2
Thus, asylum cases often turn on the IJ’s credibility determination; an ad*509verse credibility finding will doom the applicant’s claimed eligibility as a “refugee” under either method of proof. “ ‘A credibility analysis assesses the applicant’s claim only for internal consistency, detail, and plausibility, typically demonstrated by background evidence concerning general country conditions, if available....’” Gjerazi, 435 F.3d at 808 (quoting Capric, 355 F.3d at 1085); see also 8 U.S.C. § 1158(b)(l)(B)(iii).3 Corroboration is generally not required to meet the petitioner’s burden of proof unless the IJ finds the testimony not credible without it. Capric, 355 F.3d at 1085-86 & n. 4 (discussing in which situations corroboration is required to meet petitioner’s burden of proof); see also 8 C.F.R. § 208.13(a) (“The testimony of the applicant, if credible, may be sufficient to sustain the burden of proof without corroboration.”) (emphasis added).
In this case, the IJ found Musollari not credible, resting this determination on a number of factors, only some of which (as we will explain) are supported by the record. First, the IJ viewed Musollari’s claim that he was interrogated and threatened after serving as an election observer with skepticism, saying such claims were extremely common amongst applicants from Albania. Relatedly, the IJ disbelieved Musollari’s claim that the Socialist Party asked him in November 2000 to manipulate an election that had occurred the month before. The IJ also thought Musollari’s arrests in 1997 and 1998 were not significant enough to warrant detailed consideration, Next, the IJ noted that Musollari’s testimony about the Socialist Party seizing control of the government in 1997 through force and violence was “diametrically opposed” by information in country reports and other sources of historical data establishing that the Democratic government collapsed that year because of scandal and chaos associated with the failure of large “pyramid schemes.” The IJ also faulted Musollari’s failure to produce corroboration for his two arrests and the claimed ransacking of his home by the police. Finally, the IJ noted that Mu-sollari conceded he lied to American officials about his purpose for coming to the United States in order to obtain a visa.
As we have noted, our review of the record reveals a number of mistakes in the IJ’s reasoning. Musollari testified that he was an election observer in October of 2000 and was detained and threatened by police in November of 2000 based on this political activity. The IJ found this implausible based in part on his personal experience with Albanian asylum seekers — 90% of whom, the IJ said, claim to have been Albanian election observers. The IJ was entitled, based on his experience adjudicating these claims, to question Musollari further on the details of his appointment and service as an election observer — and should have done so — but this in itself is an insufficient ground on which to rest an adverse credibility finding.
The IJ also erred in evaluating the reasons for Musollari’s detention in November 2000. Musollari never claimed, as the IJ asserted, that Socialist Party agents asked him to manipulate the results of the previous month’s election. Instead, he testified that they “wanted me to give all the information about the members of the democratic party or to our plans where [sic], and also tell the names of the democratic party.” Demanding the names and locations of local Democratic Party members, *510as well as information about their planned activities, is not the same thing as attempting to coerce the manipulation of a vote that occurred a month earlier. The latter might be factually implausible; the former certainly is not. See Cecaj v. Gonzales, 440 F.3d 897, 898 (7th Cir.2006) (noting that “[p]ersecution of [Albanian] Democratic Party activists during this period has been found in a number of cases”). Musollari’s testimony on this point simply is not susceptible of the interpretation the IJ placed upon it.
Finally, the IJ inexplicably stated that Musollari had not claimed he was mistreated during his two detentions in October of 1997 and September of 1998, and therefore these arrests were not serious enough to warrant further consideration.4 Musollari’s testimony was directly to the contrary, however. He stated that in October 1997 a number of Socialist Party members attempted to engage Musollari in a debate while at a restaurant. Musollari refused to be drawn in and went home. Soon thereafter, the police came to his house and started beating him before taking him to the station. Once there, he testified, he was threatened with death and was also beaten with rubber sticks. Musollari also testified that he was arrested in September 1998 on false charges of having illegal firearms in his home. He was taken to a cell where police “us[ed] violence” against him and interrogated him about his involvement in the Democratic Party. The IJ either misunderstood or mischaracterized Musollari’s testimony about his arrests.
Notwithstanding these mistakes, however, the balance of the evidence relied on by the IJ supports the adverse credibility determination. Most significantly — and this was emphasized by the BIA in affirming the Id’s decision — the IJ rightly noted that Musollari’s testimony regarding the Democratic Party’s loss of power in 1997 was wholly inconsistent with what is known to have occurred in Albania that year. Mu-sollari testified that the Socialists seized control from the Democratic Party in a violent overthrow of the government. In reality, the government of the ruling Democratic Party was brought down by the collapse of large “pyramid schemes,” which left thousands penniless. Bureau of Democracy, Human Rights & Labor, U.S. Dep’t of State, Albania Profile of Asylum Claims & Country Conditions 3 (May 2001); The Europa World Year Book Online, Albania Country Profile, Recent History (Oet.2003); Country Information & Policy Unit, U.K. Border Agency, Albania Assessment ¶ 4.7 (July 2003). Members of the Democratic Party were believed to be complied in the pyramid schemes; civil and economic chaos followed, and the government used force in an attempt to put down the demonstrations. Representatives of both the Democratic and Socialist parties agreed to abide by the results of elections in June and July of 1997, which, as we have noted, the Socialists swept. Bureau of Democracy, Human Rights & Labor, U.S. Dep’t of State, Albania Profile of Asylum Claims & Country Conditions 3 (May 2001); The Europa World Year Book Online, Albania Country Profile, Recent History (Oct.2003).
Musollari attempts to minimize the stark differences between his testimony and the factual history by arguing that he simply gave “his impression about what transpired.” But this sort of dramatic diserep-*511ancy between an asylum seeker’s testimony and the established background facts may form the basis of an IJ’s adverse credibility finding. See Capric, 355 F.3d at 1085. Although we have repeatedly cautioned against overreliance on generalized information in country profiles or State Department country reports, see Oy-ekunle v. Gonzales, 498 F.3d 715, 716 (7th Cir.2007); Dong v. Gonzales, 421 F.3d 573, 578 (7th Cir.2005), it is permissible for an IJ to contrast an asylum applicant’s testimony with specific historical facts provided in a country report, see Huang v. Gonzales, 453 F.3d 942, 947 (7th Cir.2006), and that is what the IJ did here.
Once Musollari’s credibility was called into question, the IJ was entitled to consider the lack of corroboration for other aspects of his testimony. See Capric, 355 F.3d at 1085-86 (“[I]f the IJ finds the testimony to be incredible, then a convincing explanation of the discrepancies or extrinsic- — and credible — corroborating evidence is required.”); see also Ikama-Obambi v. Gonzales, 470 F.3d 720, 725 (7th Cir.2006) (“[A]n IJ may disbelieve an applicant because she fails to provide corroborating evidence, and subsequently deny her claim.”). Despite having nearly two and a half years to compile his case, Musollari presented no evidence to corroborate the core factual aspects of his claim: his arrests in 1997 and 1998 — during which he testified that he was mistreated — or the ransacking of his house by the police in September of 1997. The IJ noted that corroborating testimony or affidavits from family or friends might reasonably have been obtained “insofar as Albania is not [now] experiencing any civil strife or war and that there are regular commercial contacts and mail contacts with that country.”
Finally, the IJ relied on Musollari’s admission that he gave false information to the American Embassy when applying for a travel visa. “Inconsistencies that do not relate to the basis of the applicant’s alleged fear of persecution are less probative than inconsistencies that do.” Balogun, 374 F.3d at 504; see also Korniejew v. Ashcroft, 371 F.3d 377, 383-84 (7th Cir. 2004) (finding that a discrepancy on a collateral matter cannot “form the basis for an adverse credibility finding” on its own). “Nevertheless, multiple misrepresentations to Agency officials can serve as a factor in the credibility calculus.... ” Balogun, 374 F.3d at 504. Accordingly, although the errors in the IJ’s analysis give us pause, we conclude that the evidence and sufficent “specific, cogent reasons” support the adverse credibility finding; the record does not compel a contrary conclusion.
The Musollaris also challenge the IJ’s refusal to hear new evidence on remand, but this argument is a nonstarter. They never explained to the IJ or the BIA what this new evidence might be, nor have they favored us with a description. Their failure to do so is fatal to the argument. Rehman v. Gonzales, 441 F.3d 506, 509 (7th Cir.2006) (“[C]ourts do not set aside agencies’ decisions unless mistakes cause prejudice, and how could we ascertain prejudice without an offer of proof or some substitute?”). The Musollaris’ persistent failure to identify their “new evidence” leads to the inevitable conclusion that “there is nothing more to offer.” Id. The petition for review must therefore be Denied.
. Vergjinush Musollari’s application was derivative of her husband’s. See 8 U.S.C. § 1158(b)(3)(A) ("A spouse or child ... of an alien who is granted asylum under this subsection may, if not otherwise eligible for asylum under this section, be granted the same status as the alien if accompanying, or following to join, such alien.”).
. In order to obtain relief under 8 U.S.C. § 1231(b)(3) for withholding of removal, an applicant must “demonstrate a clear probability of persecution,” which is a more demanding burden than that for asylum. Balogun, 374 F.3d at 508. Similarly, the standard for withholding of removal under the CAT is that it is "more likely than not” that the applicant will be tortured if returned. 8 C.F.R. § 1208.16(c)(2). This too is higher than the burden for asylum. See Dandan v. Ashcroft, 339 F.3d 567, 575 n. 7 (7th Cir.2003). Thus, if the petitioners failed to prove their claim for asylum because Musollari’s testimony lacked credibility, the other claims must also fail.
. Section 1158(b)(1)(B) was added by the REAL ID Act of 2005, Pub.L. No. 109-13, § 101(a)(3), and applies only to applications for asylum that were filed on or after May 11, 2005. Id. § 101(h)(2); see also Oyekunle v. Gonzales, 498 F.3d 715, 717-18 (7th Cir. 2007). Musollari’s application was received on February 1, 2002.
. The IJ also believed that the second arrest occurred in July 1998; in his brief Musollari calls this a "disturbing” mistake because he was “arrested and beaten in October of 1998.” Based on our review of the record, both dates are incorrect. Musollari testified that the second arrest occurred on September 14, 1998.