Erubes Ramirez-Martinez appeals his 120-month sentence for conspiracy to possess with intent to distribute heroin, and attempted possession with intent to distribute heroin, both in violation of 21 U.S.C. § 846. Martinez-Ramirez argues that the district court erred in denying him a safety-valve reduction of his sentence. He asserts that the district court erred (1) by finding that his statements in support of a safety valve reduction were untruthful; and (2) by denying him a continuance to obtain evidentiary support for his statements.

The “safety-valve” provision, provided in U.S.S.G. § 5C1.2, requires a district court to sentence a defendant without regard to any statutory minimum if, inter alia, “the defendant has truthfully provided to the Government all information and evidence the defendant had concerning the offense____” U.S.S.G. § 5C1.2(5) (emphasis added). The question of whether the defendant’s safety-valve statement is truthful is a factual finding, which we review for clear error. United States v. Brownlee, 204 F.3d 1302, 1305 (11th Cir. 2000).

Here, Ramirez-Martinez initially told the court that he was involved in a conspiracy with an unnamed uncle and cousin. However, when pressed to identify these individuals, he changed his story and took the position that his coconspirators were a man called “La Fania” in Baltimore and several unnamed individuals in New York. We have previously held that while lies and omissions do not automatically disqualify a defendant from safety valve relief, a defendant’s prior lies may be relevant as “part of the total mix of evidence for the district court to consider in evaluating the completeness and truthfulness of the defendant’s [final] proffer.” Id. (internal quotation marks omitted). We therefore find that the district court properly considered Ramirez-Martinez’s prior falsehoods in determining that he was untruthful. Further, in light of these earlier statements, we conclude that Ramirez-Martinez has not met his burden of showing that the district clearly erred in finding *938 him ineligible for safety-valve relief and accordingly, we affirm. United States v. Cruz, 106 F.3d 1553, 1557 (11th Cir. 1997) (finding that a defendant bears the burden of establishing the truthfulness of his statement).

Ramirez-Martinez also argues that the district court erred in denying him a continuance to seek further evidentiary support for his statement. We review a district court’s denial of a motion to continue sentencing for abuse of discretion. United States v. Lee, 427 F.3d 881, 896 (11th Cir. 2005), cert. denied, 546 U.S. 1221, 126 S.Ct. 1447, 164 L.Ed.2d 145 (2006). The defendant has the burden to demonstrate that “the denial was an abuse of discretion and that it produced specific substantial prejudice.” United States v. Smith, 757 F.2d 1161, 1166 (11th Cir. 1985). First, we reject as irrelevant and unsupported, Ramirez-Martinez’s argument that the motion was denied because the district court was in a hurry. Second, we agree with the district court that, in light of Ramirez-Martinez’s repeated false statements, a continuance would only delay the inevitable denial of a safety-valve reduction. We therefore find that Ramirez-Martinez was not prejudiced by the denial of his motion and accordingly, we affirm the decision below.

AFFIRMED.