
608 F.3d 1010 (2010)
UNITED STATES of America, Appellee,
v.
Jose E. CASTELLANOS, also known as Jose Navarrete, also known as Pescado, also known as Fish, also known as Guillermo Lujan, Appellant.
No. 09-1456.
United States Court of Appeals, Eighth Circuit.
Submitted: February 12, 2010.
Filed: July 1, 2010.
*1013 Stephen C. Moss, Asst. Fed. Public Defender, Kansas City, MO, argued (Raymond C. Conrad, Jr., Fed. Public Defender, on the brief), for appellant.
Kathleen D. Mahoney, Asst. U.S. Atty., Kansas City, MO, argued (Matt J. Whitworth, Acting U.S. Atty., on the brief), for appellee.
Before RILEY,[1] Chief Judge, SMITH and SHEPHERD, Circuit Judges.
RILEY, Chief Judge.
This is the second time this case has come before our court for review. In United States v. Castellanos, 518 F.3d 965 (8th Cir.2008)(Castellanos I), Castellanos appealed the district court's denial of his motion to suppress evidence obtained during a post-warrant search of his residence, claiming the warrant was based upon an unlawful pre-warrant search. We held a portion of the pre-warrant search was unlawful, and we reversed in part and remanded for further proceedings. On remand, the district court found the evidence obtained during the post-warrant search was admissible under the independent source doctrine. Castellanos appeals, claiming the government (1) waived the right to raise the independent source doctrine on remand, and (2) failed to prove the warrant was based on an independent source.

I. BACKGROUND
Law enforcement officers received information from a confidential informant and other sources that Castellanos was in the United States illegally, Castellanos was selling large quantities of methamphetamine from his trailer residence, and a member of Castellanos's family had been kidnapped and killed. On February 23, 2006, at approximately 6:15 a.m., six law enforcement officers, including Detective Luis Ortiz (Detective Ortiz) with the Kansas City, Missouri, Police Department, and Special Agent Tracy Raggs (Agent Raggs) of U.S. Immigration and Customs Enforcement, went to Castellanos's residence.
Upon arrival, officers found the door partially open, and because they had information about a possible kidnaping and murder, they entered the residence to determine the welfare of the occupants. Finding no one inside, the officers exited to the porch, where they observed Castellanos drive a pick-up truck into the residence's parking lot. When Castellanos saw the officers, he began to drive away. Agent Raggs followed Castellanos in a car and stopped Castellanos for weaving his car. Detective Ortiz was also present. The officers noticed Castellanos was intoxicated and had urinated on himself. Initially, Castellanos refused to identify himself, but he eventually provided the officers with the name Guillermo Lujan. Castellanos said he had identification at home. Detective Ortiz asked Castellanos for consent to search his trailer and pick-up truck, but Castellanos did not reply.
The officers drove Castellanos to his residence to verify his identity. Castellanos opened the unlocked door of his residence, and Castellanos did not object when Agent Raggs and Detective Ortiz followed him inside. Castellanos refused to say his name and said "no" to Detective Ortiz's request to search the residence. Agent Raggs again asked Castellanos for his identification, and Castellanos "flipped his hand" in the direction of his bedroom. Agent Raggs entered Castellanos's bedroom and searched a dresser and a chest of drawers, but did not locate any identification. Agent Raggs did notice a notebook on the dresser with monetary figures *1014 written on it, and saw similar papers in the living room, including a paper taped to the wall with names, numbers and monetary figures. Agent Raggs testified the document on the wall appeared to be a drug transaction ledger.
Eventually, Agent Raggs noticed a wallet on a bookshelf next to Castellanos, and retrieved identification from the wallet bearing the name of Guillermo Lujan. Agent Raggs asked Castellanos if his name were Guillermo Lujan, and Castellanos repeatedly responded, "what's on the ID?" Agent Raggs also asked Castellanos about his immigration status, and Castellanos admitted he was in the country illegally. Detective Ortiz decided to apply for a search warrant, and during the execution of the warrant, law enforcement officers found evidence of drug dealing. Castellanos was then charged with federal drug and firearm related offenses.
Castellanos filed a motion to suppress, claiming, among other things, that all evidence found in execution of the search warrant should be suppressed because the warrant was based upon observations of police during an unlawful search of Castellanos's home. The district court, adopting the magistrate judge's report and recommendation, granted Castellanos's motion to suppress as to the search of Castellanos's pick-up truck for reasons unrelated to this opinion, and denied the motion to suppress in all other respects.
Castellanos entered a conditional guilty plea to conspiracy to distribute 500 grams or more of methamphetamine, in violation of 21 U.S.C. §§ 841(a)(1), (b)(1)(A) and 846, reserving the right to appeal the denial of his motion to suppress. Castellanos then appealed to our court, claiming law enforcement officers illegally entered and searched his home. Castellanos also argued, for the first time on appeal, that "[e]ven if the warrantless entry into his home was reasonable, police had no reasonable basis by which to conclude that [Castellanos] had impliedly consented to a search of his bedroom for identification."
We concluded the law enforcement officers lawfully entered Castellanos's residence, but Castellanos was too intoxicated to consent to a search of his bedroom. Castellanos I, 518 F.3d at 970. We therefore reversed the district court's denial of Castellanos's motion to suppress "with respect to the evidence seized from Castellanos's bedroom," affirmed the district court's ruling in all other respects, and "remanded to the district court for further proceedings consistent with [our] opinion." Id. at 972.
On remand, Castellanos filed a supplemental motion to suppress, arguing the government waived its right to raise the independent source doctrine. He also claimed the scope of the remand should be limited to a determination, based on the existing evidentiary record, whether evidence obtained following the search of Castellanos's bedroom constituted fruit of the poisonous tree. In response, the government suggested the court hold a hearing to determine whether the police would have sought the warrant even if the unlawful entry into the bedroom had not occurred, and whether the information obtained through the unlawful entry impacted the court's decision to issue the search warrant. The magistrate judge found (1) the government did not waive its right to assert the independent source doctrine, (2) redacting the information obtained by police during the unlawful search of Castellanos's bedroom did not affect the probable cause of the affidavit used to obtain a search warrant, and (3) additional evidence was needed to determine whether the illegal search motivated the officers to procure a search warrant.
On December 1, 2008, the magistrate judge held an evidentiary hearing. Detective *1015 Ortiz testified the records observed in the bedroom did not impact his decision to seek a search warrant. Based upon Detective Ortiz's testimony, the magistrate judge drafted a second report, recommending the district court deny Castellanos's supplemental motion to suppress based upon a finding that "the officers would have requested a search warrant even without having seen the logs which appeared to be drug sales records in defendant's bedroom." On February 17, 2009, the district court adopted the magistrate judge's second report and recommendation, and denied Castellanos's supplemental motion to suppress.
Castellanos now appeals, claiming the government waived its right to rely on the independent source doctrine because the government did not raise the doctrine in the initial proceeding, and the district court lacked jurisdiction on remand to reopen the evidentiary record and allow the government to litigate a new theory of admissibility for the challenged evidence. In the alternative, Castellanos argues, "[e]ven if the government did not waive the independent source exception," the government failed to prove Detective Ortiz would have included information regarding the drug trafficking notations observed in the living room absent the unlawful observation of similar notations in the bedroom.

II. DISCUSSION

A. Jurisdiction to Reopen the Evidentiary Record
The law of the case doctrine and the related concept of waiver are prudential rather than jurisdictional, and neither rule is an absolute bar to appellate review. See Kessler v. Nat'l Enters., Inc., 203 F.3d 1058, 1059 (8th Cir.2000); Crocker v. Piedmont Aviation, Inc., 49 F.3d 735, 739-40 (D.C.Cir.1995). The district court, therefore, did not lack jurisdiction to decide those issues left open by our mandate, see United States v. Hessman, 493 F.3d 977, 981 (8th Cir.2007) (noting a district court is again vested with jurisdiction upon receipt of our judgment), nor did the district court abuse its discretion by reopening the record to hold an evidentiary hearing, see Jones & Laughlin Steel Corp. v. Pfeifer, 462 U.S. 523, 552, 103 S.Ct. 2541, 76 L.Ed.2d 768 (1983) ("On remand, the decision on whether to reopen the record should be left to the sound discretion of the trial court.").

B. Standard of Review
When reviewing a district court's denial of a suppression motion, we review the court's factual findings for clear error and its legal conclusions de novo. See United States v. Bell, 480 F.3d 860, 863 (8th Cir.2007); United States v. Solomon, 432 F.3d 824, 827 (8th Cir.2005). We will affirm the district court's decision to deny a motion to suppress unless it is unsupported by substantial evidence on the record; reflects an erroneous view of applicable law; or after a thorough review of the record, we have a definite and firm conviction that a mistake has been made. See Bell, 480 F.3d at 863.

C. New Issue on Remand

1. Earlier Proceedings
In order to determine the propriety of the district court's actions on remand, we must first consider what transpired in the earlier proceedings. First, Castellanos filed a motion to suppress, which the district court denied in large part. Castellanos then appealed, raising for the first time the issue that, "[e]ven if the warrantless entry into his home was reasonable, police had no reasonable basis by which to conclude that [Castellanos] had impliedly consented to a search of his bedroom for identification."
*1016 Despite the apparent waiver of Castellanos's argument as untimely, this court adopted Castellanos's position, and found Castellanos was too intoxicated to consent to the officers' entry into his bedroom. Castellanos I, 518 F.3d at 970. We then reversed the district court "with respect to the evidence seized from Castellanos's bedroom," and directed that "the evidence seized during the unlawful search of Castellanos's bedroom must be suppressed." Id. at 972. We affirmed the district court's ruling in all other respects and remanded the case for further proceedings consistent with our opinion. Id.
On remand, the court below was left with the task of deciphering our mandate in Castellanos I. The magistrate judge recognized our court ordered all "evidence seized during the unlawful search of Castellanos's bedroom be suppressed," when, in fact, no evidence had actually been seized during the unlawful search. Instead, the record demonstrates Agent Raggs observed a notebook in the bedroom with monetary figures written on it. The magistrate judge concluded, "[b]ecause there is no evidence to suppress ..., it seems logical to conclude that the court of appeals intended the analysis to go further, i.e., whether the suppression of that information would affect the outcome." Thus, the magistrate judge found the next step in the process must be to determine whether officers would have had sufficient probable cause to obtain a warrant absent the illegal search of the bedroom. The magistrate judge's interpretation of our indistinct holding was sound and "consistent with [our] opinion" in Castellanos I, 518 F.3d at 972.
In conducting this analysis, the magistrate judge rejected Castellanos's contention the government waived the right to raise the independent source doctrine. The magistrate judge recognized strict application of waiver principles, as applied to Castellanos, would result in denial of relief because Castellanos himself had failed to assert properly that the entry into his bedroom was illegal before the appeal. The magistrate judge decided, "[b]ecause the government could not foresee the Eighth Circuit's ruling ... the government has raised the independent source doctrine at the earliest practicable time in this case and therefore has not waived its right to assert that doctrine." After an evidentiary hearing, the magistrate judge found the independent source doctrine applied. Adopting the magistrate judge's report and recommendation, the district court denied Castellanos's supplemental motion to suppress all the evidence found pursuant to the search warrant.

2. Law of the Case and the Mandate Rule
"`Law of the case terminology is often employed to express the principle that inferior tribunals are bound to honor the mandate of superior courts within a single judicial system.'" United States v. Bartsh, 69 F.3d 864, 866 (8th Cir.1995) (quoting 18B Charles A. Wright, Arthur R. Miller & Edward H. Cooper, Federal Practice & Procedure § 4478 (1981 & Supp.1995)). "When an appellate court remands a case to the district court, all issues decided by the appellate court become the law of the case, and the district court on remand must `adhere to any limitations imposed on its function ... by the appellate court.'" Id. (quoting United States v. Cornelius, 968 F.2d 703, 705 (8th Cir.1992)) (internal citation omitted). Absent "instructions to hold further proceedings, a district court has no authority to re-examine an issue settled by a higher court." Bethea v. Levi Strauss & Co., 916 F.2d 453, 456 (8th Cir.1990). In contrast, "[w]hile a mandate is controlling as to matters within its compass, on the remand a lower court is free as to other issues." *1017 Sprague v. Ticonic Nat'l Bank, 307 U.S. 161, 168, 59 S.Ct. 777, 83 L.Ed. 1184 (1939).
An application of this doctrine is visible in Cornelius, 968 F.2d at 704-06. In that case, Cornelius appealed his sentence, and the government cross-appealed the district court's finding that Cornelius was not an armed career criminal under 18 U.S.C. § 924(e). Id. at 704. This court reversed and remanded for resentencing on the issue raised in the government's cross-appeal. Id. (discussing United States v. Cornelius, 931 F.2d 490 (8th Cir.1991)). At resentencing, Cornelius argued one of his prior convictions was based on an invalid guilty plea and could not be used to enhance his sentence for being an armed career criminal. Id. Cornelius also argued two of the convictions were related cases and therefore could not be used to find he was a career offender under United States Sentencing Guidelines § 4B 1.1. Id. The district court held it could not consider these new issues on remand. Id. at 704. This court reversed because "[w]e did not limit the district court's further determination of whether Cornelius was an armed career criminal," and "the district court was free to consider any new arguments raised at the resentencing as to whether Cornelius was an armed career criminal that could have been considered at the first hearing." Id. at 706. However, we affirmed the district court's "refus[al] to consider new evidence relating to Cornelius' [s] sentence enhancement as a career offender because that determination was not before the district court on remand." Id.; cf. United States v. Ticchiarelli, 171 F.3d 24, 32-33 (1st Cir.1999) (finding defendant had not waived an issue he raised for the first time during resentencing because the arguments were made newly relevant by the court of appeals' decision and the defendant did not have "sufficient incentive to raise the issue in the prior proceedings").
In the present case, our mandate left several issues open for the district court to decide and expressly ordered the district court to hold further proceedings consistent with our opinion. Castellanos I, 518 F.3d at 972. The district court limited its review and only considered one ultimate issuewhether the information obtained during the unlawful search of the bedroom impacted the validity of the search warrant. We agree with the district court's reading of our mandate, and we commend the district court, and particularly the magistrate judge, for its cogent analysis and commitment to following the ill-defined directives of this court.

3. Waiver

a. New Issue v. New Argument
Although lower courts are free to decide new issues left open on remand, this court must also consider whether an issue not previously raised is deemed waived, and therefore, not within the scope of remand. See Sprague, 307 U.S. at 168-69, 59 S.Ct. 777; United States v. Husband, 312 F.3d 247, 250 & n. 3 (7th Cir. 2002) (declaring "any issue that could have been but was not raised on appeal is waived and thus not remanded"). Not every new argument, or shift in approach, constitutes the raising of a new issue. See Weitz Co. v. Lloyd's of London, 574 F.3d 885, 890-91 (8th Cir.2009); Universal Title Ins. Co. v. United States, 942 F.2d 1311, 1314-15 (8th Cir.1991). The government argues it did not raise a new issue on remand, but merely continued to advance the proposition "that the search warrant was based upon adequate probable cause gained from lawful entry into the trailer." This argument has merit.
In United States v. Duchi, 906 F.2d 1278, 1285 (8th Cir.1990) (Duchi I), this court "reverse[d] Duchi's convictions on all counts because the evidence used to convict *1018 him was the fruit of a warrantless entry without exigent circumstances." We noted the government was free to retry the appellant, but the government would have to prove its case "without the benefit of the evidence gained from unconstitutionally entering his home." Id. On remand, the government attempted to argue, for the first time, that the evidence was admissible under the inevitable discovery doctrine. See United States v. Duchi, 944 F.2d 391, 392 (8th Cir.1991) (Duchi II). The district court ruled the government could not argue a new ground for the introduction of evidence when this court already held that evidence had been illegally obtained. Id. In Duchi II, our court affirmed the district court, in relevant part, declaring, "[t]he Government may not advance during a second trial previously unasserted grounds for the admissibility of evidence seized in a warrantless search which an appeals court has concluded should have been suppressed on the basis of arguments made at the first trial." Id.
Castellanos cites Duchi II in his brief for the proposition that "if alternative grounds for admission existed, then the Government should have presented those theories in the prior case." Id. at 393. However, Duchi II is distinguishable from Castellanos's case, and the reasoning of Duchi II supports the government's position on appeal. In Duchi I, 906 F.2d at 1285, our court announced the evidence at issue had been illegally obtained and was inadmissible in the district court. We did not remand for further proceedings on the issue of admissibility. See id. In contrast, in Castellanos I, 518 F.3d at 972, this court found the evidence obtained in the bedroom during the illegal search was inadmissible, but we did not make any findings as to the admissibility of the remaining evidence found in Castellanos's residence, and we remanded for further proceedings, consistent with our opinion.
We agree with the proposition set forth in Duchi II that an "issue" addressed by a court "is not the particular theory that would support the admission of evidence, but the broader question concerning the admissibility itself." Duchi II, 944 F.2d at 393. Thus, the "issue" decided by this court in Duchi I was the overarching question of "whether the search was constitutional," not the narrower question of "whether exigent circumstances justified the search." Id. Applying this reasoning to Castellanos's case, the issue raised by the parties below and addressed by this court in Castellanos I was the constitutionality of the entry and search of Castellanos's residence. The government then did not raise a new "issue" on remand when it argued the evidence was admissible under the independent source doctrine, but merely formulated a new argument in support of the position maintained by the government in each proceeding.

b. Application of the Waiver Doctrine to Castellanos
In his brief, Castellanos repeatedly cites cases which stand for the proposition that issues not raised before the district court are waived, and therefore, cannot be considered by this court on appeal. "The purpose of the rule is to inform promptly the trial judge of possible errors so that he may have an opportunity to reconsider his ruling and make any changes deemed desirable." Morrow v. Greyhound Lines, Inc., 541 F.2d 713, 724 (8th Cir.1976). However, we are not currently faced with a scenario where an issue has been raised for the first time on appeal. In this case, the district court considered the independent source doctrine when it was raised before the district court on remand. Therefore, the only purposes which would be served by invoking the waiver doctrine here would be to prevent "piecemeal appeals," see *1019 United States v. Carter, 490 F.3d 641, 645 (8th Cir.2007), and to promote judicial efficiency, see Morris v. American Nat'l Can Corp., 988 F.2d 50, 52 (8th Cir.1993). Neither of these interests would be served by finding the government waived its use of the independent source doctrine under the facts of this case. Cf. Universal Title, 942 F.2d at 1314 (noting appellate courts have the discretion to consider a new issue on appeal when the proper resolution of the case is beyond any doubt, or if injustice might otherwise result).
"The general rule is that, `where an argument could have been raised on an initial appeal, it is inappropriate to consider that argument on a second appeal following remand.'" Kessler, 203 F.3d at 1059. However, "appellate courts should not enforce the rule punitively against appellees, because that would motivate appellees to raise every possible alternative ground and to file every conceivable protective cross-appeal, thereby needlessly increasing the scope and complexity of initial appeals." Id.; see also Crocker, 49 F.3d at 739-41; Field v. Mans, 157 F.3d 35, 41-42 (1st Cir.1998). It is unclear when Castellanos believes the government should have argued the independent source doctrine for the first time. Although the government should be required to raise alternative theories for the admission of evidence at the outset, the government cannot be expected to respond to arguments in the district court which were not actually raised by the defendant until the appeal.
In Field, 157 F.3d at 37, 40-42, a bankruptcy court held in favor of the appellee, and an appeal was pursued to the Bankruptcy Appellate Panel, and then to the First Circuit. The First Circuit recognized that "to preserve an alternative theory, an appellee might in some situations be required to raise the point in its appellate briefs." Id. at 41. However, the court declined to find the appellee waived an alternative argument because it would be "extremely unrealistic" to expect appellee's counsel to argue "an alternate theory in support of the lower court's judgment." Id. The First Circuit continued, "We are loath to find that [the appellee] waived the extension issue merely by failing to file either a procedurally dubious cross-appeal in the district court and in this court, or to brief and argue what, to any attorney, might have seemed an entirely redundant point." Id. at 41-42 (internal citation omitted).
Although parties should present alternative arguments whenever sound strategy dictates, the government in this case was not required to anticipate every possible outcome on appeal and formulate a responsive argument for each alternative. "[T]he principle that a party who failed to raise an argument in its initial appeal is held to have waived its right to raise that argument on remand or on a second appeal .... must be limited to issues appropriate to be raised on appeal." Robinson v. Johnson, 313 F.3d 128, 141 n. 5 (3d Cir.2002). "It does not require a party to raise an issue that had not been previously treated or even raised in the district court." Id. "Issues that arise anew on remand are generally within the scope of the remand." Husband, 312 F.3d at 251 n. 4; see also United States v. Morris, 259 F.3d 894, 898 (7th Cir.2001) ("[O]n remand and in the absence of special circumstances, a district court may address only (1) the issues remanded, (2) issues arising for the first time on remand, or (3) issues that were timely raised before the district and/or appellate courts but which remain undecided.").
Under the facts of this case, the application of the independent source doctrine was an argument arising for the first time *1020 on remand. Cf. United States v. Khabeer, 410 F.3d 477, 483-84 (8th Cir.2005) (remanding to the district court to consider the application of the independent source doctrine for the first time); United States v. Namer, 680 F.2d 1088, 1097-98 (5th Cir.1982) (same). In Castellanos I, we explicitly directed the district court to engage in further proceedings consistent with our opinion. Implicit in that order was an expectation that the district court would consider arguments raised by both parties as to how the exclusion of the information obtained during the illegal search of the bedroom would impact the validity of the search warrant. The government raised the independent source doctrine at the earliest practicable time, and did not waive the application of the independent source doctrine on remand. The district court did not err in relying upon the independent source doctrine when denying Castellanos's supplemental motion to suppress.

D. Applicability of the Independent Source Doctrine
Castellanos argues the district court erred in finding Detective Ortiz would have applied for the search warrant absent the illegal entry into the bedroom because "the record did not establish that the information regarding the drug trafficking notations on the paper in the living room was obtained independently of the unlawful observations made by [Agent] Raggs during the search of [Castellanos's] bedroom." We disagree.
In his second report and recommendation to the district court, the magistrate judge listed various facts which supported Detective Ortiz's decision to obtain a warrant, separate and apart from either of the drug transaction ledgers observed in Castellanos's home, e.g., multiple confidential informants confirmed pertinent details and Detective Ortiz presented his expert opinion on the applicable illegal drug business. The magistrate judge emphasized one of the drug transaction ledgers had been taped to the wall in the living room, kitchen, and dining room common area, and was in plain view to anyone standing where Detective Ortiz was positioned in the living room. Thus, the magistrate judge concluded the drug transaction ledger Agent Raggs saw in the bedroom was duplicative, and Detective Ortiz would have applied for the search warrant even if the drug transaction ledger had not been viewed in the bedroom during the illegal search. The magistrate judge's findings are supported by substantial evidence in the record, and the district court did not clearly err in adopting the magistrate judge's factual findings. See United States v. Swope, 542 F.3d 609, 613 (8th Cir.2008) (standard of review).

III. CONCLUSION
We affirm the judgment of the district court.
NOTES
[1]  The Honorable William Jay Riley became Chief Judge of the United States Court of Appeals for the Eighth Circuit on April 1, 2010.
