FLAUM, Circuit Judge.

Chicago police arrested James Selvie for weapons crimes stemming from his possession of a loaded handgun. While in custody, he contacted his girlfriend, Juvona Robinson, and asked her to file a complaint with the Chicago Police Department ("CPD"), alleging that his arresting officers planted the gun on him and arrested him falsely. Robinson did so, and CPD initiated an investigation into Selvie's allegations. As part of its investigation, CPD contacted Robinson, who immediately recanted her complaint and confessed that she had no actual knowledge of what transpired during Selvie's arrest. CPD terminated its investigation.

Federal authorities ultimately assumed jurisdiction over Selvie's case and charged him with being a felon in possession of a firearm, 18 U.S.C. § 922(g). He pled guilty pursuant to a plea agreement. He appeals his sentence, arguing that the district court improperly enhanced his base offense level for obstruction of justice, predicated on the false complaint he lodged with CPD. We affirm the district court's sentence.

I. Background

On May 3, 2010, Chicago police officers on patrol observed James Selvie, a known gang member, with a bulge in his waistband that they deemed suspicious. They exited their squad car to investigate further, at which time Selvie fled on foot and tossed a loaded handgun onto a nearby porch. The officers arrested Selvie and recovered the gun.

The State's Attorney's Office charged Selvie with various weapons offenses. The charges constituted a parole violation, and he remained in custody at the Statesville Correctional Facility.

On May 8, 2010, Selvie's girlfriend called CPD to file a complaint. She alleged that Selvie's arresting officers planted the gun on him and arrested him falsely. Sergeant William Gentile was assigned to investigate her allegations. When he contacted her, she immediately volunteered that she made the complaint at Selvie's request, that she was not present when he was arrested, and that she lacked any first-hand knowledge about the arrest. She also informed Gentile that she could not substantiate her complaint, refused to provide a sworn statement, and requested that he terminate the investigation. Gentile closed the investigation.

In August 2010, the United States Attorney's Office for the Northern District of Illinois indicted Selvie for being a felon in possession of a firearm, 18 U.S.C. § 922(g). The state charges against him were dismissed. Selvie pled guilty to the federal charge pursuant to a plea agreement. The agreement did not contain an enhancement for obstruction of justice.

Before sentencing, Selvie's probation officer provided a Presentencing Report to the court. The officer contended that Selvie caused his girlfriend to file a false report in order to obstruct CPD's investigation. He recommended a two-level increase to the base offense level. Selvie objected to the proposed enhancement, arguing that his girlfriend never suggested that she witnessed his arrest and that his conduct did not obstruct justice under Section 3C1.1 of the Sentencing Guidelines.

At sentencing, the government agreed that Selvie's conduct did not amount to obstruction. Yet, the district court, signaling that it found significant Selvie's attempt to induce a third party to file a complaint, instructed the government to brief the issue and continued the hearing. The government filed the requested brief, in which it reversed its position and endorsed an obstruction enhancement. Selvie, it concluded, attempted to intimidate or influence the arresting officers into withholding their testimony by inducing his girlfriend to file a complaint against them. Subsequently, the probation department amended the Presentencing Report, withdrawing its request for an obstruction enhancement. It explained that the enhancement was inappropriate because, in light of the fact that Selvie's girlfriend did not witness his arrest, Selvie's putative attempt to obstruct the investigation was ill-conceived, had little chance of success, and was quickly abandoned.

Nevertheless, when sentencing resumed, the district court found that Selvie obstructed justice and enhanced his base offense level by two levels. His guideline range increased from 37-46 months to 46-57 months. The court sentenced Selvie to 51 months' imprisonment.

II. Discussion

We review for clear error a district court's factual findings that underlie a sentencing enhancement. See United States v. Pellmann, 668 F.3d 918, 926 (7th Cir. 2012). We review a district court's decision to enhance a sentence based on those facts de novo. See id.

A. The District Court Did Not Clearly Err in Its Findings of Fact

At sentencing, the district court found that Selvie planned and attempted to induce false testimony from a fabricated witness in order subvert the government's ability to prove the charges against him. It stated:

This behavior, it concluded, constituted obstruction of justice.

We will disturb the district court's findings as clearly erroneous only if our review of the record leaves us with "the definite and firm conviction that a mistake has been committed." United States v. Littrice, 666 F.3d 1053, 1060 (7th Cir.2012) (quoting United States v. Severson, 569 F.3d 683, 689 (7th Cir.2009)). The record does not support that assessment.

Selvie does not dispute that he called Juvona Robinson and asked her to file a complaint against his arresting officers. Nor does he dispute that he fabricated the content of that complaint, in which he alleged that the arresting officers planted the recovered gun, framed him for, inter alia, possession of a firearm, and arrested him falsely. Indeed, he ultimately pled guilty to being a felon in possession of a firearm and, thus, admitted that the weapon was not planted. Since he does not contest that he called Robinson, that she filed a report per his instructions, and that the report was false, the district court did not err in accepting these facts as true and considering them as it fashioned its decision regarding an obstruction enhancement.

B. The District Court Appropriately Enhanced Selvie's Guideline Range

Selvie argues that his actions do not satisfy the criteria for obstruction of justice. He challenges, first, that he did not induce knowingly false testimony because he never asked Robinson to tell the police that she witnessed his arrest first-hand: he merely asked her to relay to the police his complaint against his arresting officers. Second, he argues, his actions did not — and could not have — impeded the prosecution against him.

Section 3C1.1 permits a two-level increase in a defendant's offense level if:

U.S. SENTENCING GUIDELINES MANUAL § 3C1.1. One means by which a defendant may earn an obstruction enhancement is by "providing a materially false statement to a law enforcement officer that significantly obstructed or impeded the official investigation or prosecution of the instant offense." Id. at cmt. n.4(G). A statement is materially false if, were it believed, it "would tend to influence or affect the issue under determination." Id. at cmt. n.6.

In this case, Selvie provided a materially false statement to the police. Although he recruited an intermediary to relay his message, he informed CPD that his arresting officers planted a gun on him when they did not do so. Were his complaint believed, it would tend to influence or affect the issue under determination — whether Selvie illegally possessed a firearm. The presence of a gun on his person or in his possession was the crux of the charge against him. Selvie, thus, misapprehends the criteria for obstruction when he argues that Robinson did not know the information she relayed to the police was false. Her intent to obstruct or impede the investigation is irrelevant. What matters is whether he intended to obstruct or impede the investigation by providing materially false information to law enforcement. Clearly he did so: he lied about the police illegally planting evidence, and he requested Robinson to serve as the mouthpiece by which he communicated the false information; his conduct underscores that he acted wilfully.

We must consider, however, whether the false information he provided "significantly obstructed or impeded the official investigation or prosecution of the instant offense." Id. at cmt. n.4(G). Selvie argues that his false complaint was ill-conceived and quickly abandoned. Law enforcement authorities, therefore, were not and could not have been deceived by his disinformation. We hold that actual deception is irrelevant to the inquiry; the government must show only that it expended time or resources on the false information.

Materially false information provided to law enforcement must actually obstruct or impede the official investigation to merit an obstruction enhancement. See id. at cmt. n.4(G). Without more, false statements to law enforcement authorities, if not made under oath, do not actually impact the investigation or prosecution. See id. at cmt. n.5(B); see also United States v. Raupp, 677 F.3d 756, 758-59 (7th Cir.2012) (noting that the Sentencing Commission's application notes are authoritative and controlling unless "plainly erroneous or inconsistent with the regulation" (quoting Stinson v. United States, 508 U.S. 36, 44-45, 113 S.Ct. 1913, 123 L.Ed.2d 598 (1993))). The government must prove "a detrimental effect upon [its] efforts to investigate or prosecute the instant offense." United States v. Griffin, 310 F.3d 1017, 1023 (7th Cir.2002); see also United States v. Hanhardt, 361 F.3d 382, 389-90 (7th Cir.2004) (interpreting Section 3C1.1's application notes to require the government to demonstrate "[s]ignificant and actual obstruction or impediment" to apply an obstruction enhancement), vacated and remanded for re-sentencing in light of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), sub nom., Altobello v. United States, 543 U.S. 1097, 125 S.Ct. 994, 160 L.Ed.2d 996 (2005). This detrimental effect, however, need not amount to a total frustration of the government's efforts. See United States v. Owens, 308 F.3d 791, 794 (7th Cir.2002) (citing United States v. Kroledge, 201 F.3d 900, 906-07 (7th Cir.2000)) ("The fact that the government's investigative efforts were not ultimately frustrated by [the defendant's] perversion of the truth should not become a boon for the defendant."). False statements prejudice an investigation when they burden law enforcement and precipitate "expended resources to track down ... false leads." Griffin, 310 F.3d at 1023; see also United States v. Wells, 154 F.3d 412, 414-15 (7th Cir.1998). Material misinformation that exerts any impact on the government's resources may elicit an obstruction enhancement.

Selvie's false complaint forced CPD to launch an investigation and send its personnel to interview Robinson. That Robinson quickly recanted does not alter the fact that CPD spent time and manpower to vet Selvie's allegations. Her candor simply saved CPD additional time and resources otherwise wasted on Selvie's lies. Accordingly, he committed obstruction, and the district court justifiedly enhanced his base offense level.

III. Conclusion

For the foregoing reasons, we AFFIRM the decision of the district court.