
628 F.3d 420 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Lawrence TAYLOR, Defendant-Appellant.
No. 10-1304.
United States Court of Appeals, Seventh Circuit.
Submitted September 23, 2010.
Decided December 21, 2010.
*422 Frank E. Schaffer (submitted), Office of the United States Attorney, South Bend, IN, for Plaintiff-Appellee.
Andrew J. McGowan, Richard H. Parsons, Office of the Federal Public Defender, Peoria, IL, for Defendant-Appellant.
Before CUDAHY, FLAUM, and WOOD, Circuit Judges.
CUDAHY, Circuit Judge.
Appellant Lawrence Taylor appeals from his sentences for bank robbery and for violating the terms of his supervised release relating to an earlier bank robbery conviction. Because the district court erred by failing to appreciate its discretion to impose the sentences either consecutively or concurrently, we remand for the court to reconsider that aspect of the sentencing package.

I. Facts and Procedural History
In 2002 Lawrence Taylor pleaded guilty to bank robbery charges and was sentenced to a term of incarceration by the U.S. District Court for the District of Minnesota. Sometime in 2007 he was placed on supervised release, but within less than a year, on August 7, 2008, he attempted to rob a bank in South Bend, Indiana. Taylor obtained money from the tellers, but the plan went awry and Taylor was arrested before he could flee the scene.
The 2008 robbery resulted in potential terms of imprisonment with respect to two criminal cases: Case number 07-CR-184, concerning Taylor's supervised release arising from the 2002 bank robbery conviction, and case number 08-CR-100, in which the Government charged Taylor with the 2008 bank robbery.
Taylor pleaded guilty to the bank robbery on May 7, 2009, and a single sentencing hearing was set for both the bank robbery and the supervised release cases. Taylor's probation officer prepared a "Summary Report of Violations" in connection with Taylor's supervised release case, which suggested an 18- to 24-month sentence. In addition, the Summary cited a policy statement within the United States Sentencing Guidelines, U.S.S.G. § 7B1.3(f), for the proposition that any term of incarceration for the supervised release violation must be made consecutive to the bank robbery sentence. Taylor did not object to this aspect of the probation officer's report.
The district court held a sentencing hearing on February 1, 2010. By this time, Taylor and the Government had stipulated to a 12-month sentence for violating the terms of his supervised release. Therefore, argument at the sentencing hearing centered around the appropriate sentence for Taylor's bank robbery conviction, which was to be much lengthier. After discussing the factors relevant to sentencing pursuant to 18 U.S.C. § 3553(a), the district court determined to impose a 168-month sentence for the 2008 robbery. Then, with respect to the supervised release sentence, the court stated,
In addition to [the bank robbery sentence discussed immediately prior], there would be the twelve months that has to run consecutive, as I understand it, the twelve months on the supervised release violation.
(Emphasis added.) Taylor did not object to this statement, nor did he ask for concurrent sentences. The district court imposed consecutive sentences for Taylor's bank robbery conviction and his supervised release violation.
Taylor noted a timely but defective appeal from his sentences. In particular, Taylor's notice of appeal indicated only the *423 case number for the bank robbery case, but not the number pertaining to his supervised release case. The notice of appeal further indicated that the appeal was from a "judgment in a criminal case entered in this action on February 1, 2010." Taylor's argument before this court is directed exclusively to the consecutive sequencing of his sentence.

II. Applicable Law
Preliminarily to sentencing questions, this case presents an issue of appellate jurisdiction, which this court is obliged to consider sua sponte, see Janky v. Lake Cnty. Convention & Visitors Bureau, 576 F.3d 356, 359 (7th Cir.2009), even where neither party argues jurisdiction is lacking, see Int'l Union of Operating Eng'rs, Local 150 v. Ward, 563 F.3d 276, 282 (7th Cir. 2009). Specifically, because Taylor failed to include the case number for his supervised release case when he filed his notice of appeal, his appeal was technically noncompliant with Fed. R.App. P. 3(c), which provides:
(1) The notice of appeal must:
(A) specify the party or parties taking the appeal ...; [and]
(B) designate the judgment, order, or part thereof being appealed[.]
Compliance with Fed. R.App. P. 3(c) is jurisdictional. See Smith v. Barry, 502 U.S. 244, 248, 112 S.Ct. 678, 116 L.Ed.2d 678 (1992); AlliedSignal, Inc. v. B.F. Goodrich Co., 183 F.3d 568, 571 (7th Cir. 1999).
Although Rule 3(c) runs to the jurisdiction of this court, the Supreme Court has explained that it is "liberally construed." Smith, 502 U.S. at 248, 112 S.Ct. 678. This court has described the appropriate inquiry to be "whether sufficient notice was given to apprise the other parties of the issues challenged." United States v. Segal, 432 F.3d 767, 772 (7th Cir.2005). In addition, we have stated that "an error in designating the judgment will not result in a loss of appeal if the intent to appeal from the contested judgment may be inferred from the notice and if the appellee has not been misled by the defect." United States v. Dowell, 257 F.3d 694, 698 (7th Cir.2001).
Moving on to the merits, a sentencing court has discretion to make a sentence consecutive or concurrent. See 18 U.S.C. § 3584(a); United States v. Campbell, 617 F.3d 958, 961 (7th Cir.2010). This includes situations where the sentence is imposed in connection with a revocation of supervised release. See United States v. Rodriguez-Quintanilla, 442 F.3d 1254, 1256 (10th Cir.2006). A sentencing court errs when it has discretion but fails to exercise that discretion. See United States v. Jackson, 546 F.3d 465, 472 (7th Cir.2008).
As noted, the probation officer's Summary Report of Violations referred to a policy statement contained in the sentencing guidelines, U.S.S.G. § 7B1.3(f), which provides as follows:
Any term of imprisonment imposed upon the revocation of probation or supervised release shall be ordered to be served consecutively to any sentence of imprisonment that the defendant is serving, whether or not the sentence of imprisonment being served resulted from the conduct that is the basis of the revocation of probation or supervised release.
(Emphasis added.) Despite this facially mandatory language, our precedents are unambiguous that the policy statements on supervised release are not mandatory. See United States v. Harvey, 232 F.3d 585, 588 (7th Cir.2000). Rather, we have explained the import of the supervised release policy statements as follows:

*424 Rather than establishing guidelines governing the revocation of supervised release, the Sentencing Commission has opted to promulgate a series of policy statements, including a Revocation Table of recommended sentencing ranges tied to the severity of a defendant's violations and criminal history category.... Although these policy statements are nonbinding, they are to be given "great weight" by the sentencing judge.
United States v. Salinas, 365 F.3d 582, 588 (7th Cir.2004).
In sum, U.S.S.G. § 7B1.3(f) reflects the U.S. Sentencing Commission's policy favoring the consecutive sequencing of a sentence imposed upon revocation of supervised release and the sentence for the offense precipitating the revocation. See U.S.S.G. § 7B1.3(f), Application Note 4; United States v. Glasener, 981 F.2d 973, 975-76 (8th Cir.1992). The Commission's supervised release policy statements are generally entitled to "great weight." We have also emphasized, however, that while the policy statements "are an `element in [the sentencing judge's] exercise of discretion,' they are not a substitute for that discretion." United States v. McClanahan, 136 F.3d 1146, 1149 (7th Cir.1998) (quoting United States v. Hill, 48 F.3d 228, 231 (7th Cir.1995)).
If a defendant fails to raise an objection at sentencing, this court will review for plain error, asking whether "(1) error occurred; (2) the error was plain; and (3) the error affected the defendant's substantial rights." United States v. Pitre, 504 F.3d 657, 661 (7th Cir.2007). This remains true when the error alleged is that the sentencing court did not appreciate the advisory nature of the sentencing guidelines. See United States v. Wilson, 481 F.3d 475, 484 (7th Cir.2007); United States v. Santiago, 428 F.3d 699, 705 (7th Cir. 2005).

III. Analysis

A. Appellate Jurisdiction
Taylor's notice of appeal was sufficient to bring his case within our jurisdiction. Taylor's intent to appeal from both components of his sentencing package may fairly be inferred from his notice of appeal, despite the fact that he only included one case number. Both sentences arose from the same set of facts, and Taylor was sentenced in both cases at the same hearing. His notice stated that he appealed from "the judgment in a criminal case entered in this action on February 1, 2010," which could refer to either sentence. This falls comfortably within the realm of technical, non-misleading noncompliance with the rules, with respect to which an appeal should be allowed.
In addition, while we are cognizant that parties cannot stipulate to jurisdiction, the position of the government is relevant because our precedents dictate that we consider whether the appellee has been misled. Here, the Government has made no argument that it was misled or otherwise prejudiced by Taylor's failure to specify both case numbers on his notice of appeal. Instead, the Government recommends that this court credit one of Taylor's arguments and remand the case. In view of the liberal construction of Fed. R.App. P. 3(c), the minor nature of Taylor's mistake, and the absence of any argument that the Government has been misled, we consider that the notice of appeal was sufficient.

B. Sentencing
We agree with Taylor and the Government that the district court erred by treating the policy statement recommendation in U.S.S.G. § 7B1.3(f) as mandating consecutive sentencing for Taylor's 2008 bank robbery case and his supervised release *425 case. As Taylor urges and the Government concedes, the sentencing court's reference to "the twelve months that has to run consecutive, as I understand it" shows without ambiguity that the sentencing court did not appreciate its discretion to make Taylor's sentences either consecutive or concurrent.
Next, we must determine the appropriate remedy for this sentencing error. Although the supervised release policy statements were advisory well before the sentencing guidelines themselves were made advisory in United States v. Booker, 543 U.S. 220, 267, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005),[1] the district court's error here is analogous to a case in which the district court failed to appreciate the advisory nature of the sentencing guidelines. In cases of that kind and in which the defendant did not raise the issue at sentencing, the remedy has been a limited remand for the district court to determine whether it would have imposed the same sentence knowing that the guidelines are not mandatory. See United States v. Paladino, 401 F.3d 471, 484-85 (7th Cir. 2005); Santiago, 428 F.3d at 705-06.
Taylor does not ask for more than this. His reply brief states,
[T]he government requests that this court affirm the individual sentences of 168 months for the robbery and 12 months for the violation of supervised release. However, in light of the error, the government also suggests that the sentencing package be remanded with instructions for the district court to reexamine whether [they] should be concurrent, partially concurrent, or consecutive. Appellate counsel for Mr. Taylor does not object to the government's proposed solution to the problems presented in this appeal.
Such a limited remand is within our authority under 28 U.S.C. § 2106, see United States v. Young, 66 F.3d 830, 835 (7th Cir.1995), is consistent with our prior practice, see United States v. Macari, 453 F.3d 926, 942 (7th Cir.2006), and is urged by the Government and accepted by Taylor.[2] Taylor is entitled to have the district court exercise its discretion as to consecutive or concurrent treatment, but this does not detract from the "great weight" ordinarily accorded to supervised release policy statements. We express no opinion as to the proper outcome.
We AFFIRM Taylor's sentences but order a LIMITED REMAND for proceedings consistent with this opinion.
NOTES
[1]  See, e.g., Harvey, 232 F.3d at 588; Hill, 48 F.3d at 231.
[2]  Taylor points out that each of his sentences was made consecutive to the other, and that as a practical matter, it only takes one consecutive sentence to make the package consecutive. He is apparently concerned that if the district court revises the consecutive nature of only the supervised release sentence, he will still be stuck with a consecutive sentence package. On remand the district court should give full effect to our decision by reconsidering the consecutive nature of both of Taylor's sentences.
