
596 F.3d 236 (2010)
UNITED STATES of America, Plaintiff-Appellee,
v.
Archie Roy JACKSON, James Bernis Midkiff, Defendants-Appellants.
No. 07-30981.
United States Court of Appeals, Fifth Circuit.
February 3, 2010.
*238 Camille Ann Domingue, Asst. U.S. Atty., Lafayette, LA, for U.S.
Wayne Joseph Blanchard, Lafayette, LA, for Jackson.
Michael Charles Piccione, Sr. (Court-Appointed), Barry & Piccione, Lafayette, LA, for Midkiff.
Before GARZA, DeMOSS and CLEMENT, Circuit Judges.
EMILIO M. GARZA, Circuit Judge:
Archie Roy Jackson and James Bernis Midkiff were convicted of charges stemming from a conspiracy to manufacture and distribute methamphetamine. Jackson challenges the district court's denial of his motion to suppress evidence found during a search in and around his home. Midkiff contends that the district court erred by increasing the quantity of drugs attributable to him for sentencing purposes and allowing the government to amend the indictment.

I
Jackson and Midkiff were indicted by a federal grand jury for their participation in a conspiracy to manufacture and distribute methamphetamine. They, along with several co-conspirators, utilized a number of remote rural locations in Louisiana to set up methamphetamine labs. They used these labs to "cook" methamphetamine, which they later distributed. In addition to the drug crimes, both men were accused of knowingly possessing a firearm in furtherance of a drug trafficking crime in violation of 18 U.S.C. § 924(c). Midkiff also was charged with being a felon in possession of a firearm in violation of 18 U.S.C. § 922(g)(1). Federal arrest warrants were issued for both men.
*239 Before Jackson was arrested, the state case agent in the federal investigation sought a search warrant for Jackson's residence from a state court judge. The agent executed an affidavit supporting the warrant application, and, based on the affidavit, the state court issued a search warrant for Jackson's residence.
Thus, at the time the officers went to Jackson's residence, they had both a state search warrant and a federal arrest warrant. When the officers entered Jackson's home, they observed him place something under the couch on which he was sitting. They quickly arrested Jackson and then conducted a sweep of the home to ensure that no one else was present. They also examined the couch and discovered that the item Jackson placed under it was a bag of marijuana.
The officers continued their search of the residence and the outdoor area surrounding the home. Inside the house, they discovered a locked safe. Jackson provided the officers with the combination to the safe, inside of which they found guns and some crushed pseudoephedrine tablets, which are used to produce methamphetamine. Outside the house, they found chemicals and equipment used in the manufacturing of methamphetamine.
Before trial, Jackson filed a motion to suppress the evidence discovered during the search of his home. The district court denied the motion. Following a jury trial both Jackson and Midkiff were convicted of, inter alia, conspiracy to distribute methamphetamine, establishment of manufacturing operations, and attempt to manufacture methamphetamine. The jury indicated on a special jury form that it found Jackson and Midkiff guilty of a conspiracy involving 50 grams or less of methamphetamine, but not guilty of a conspiracy involving 50 to 500 grams or 500 grams or more. Midkiff was also convicted of the firearms violations.
The United States Probation Officer issued a presentence report ("PSR") attributing 1,318 grams of methamphetamine to Midkiff based on extrapolation from estimates provided by co-conspirators. Midkiff filed an objection to the PSR "in its entirety," along with two other objections that are not relevant to the appeal. The Probation Officer responded to the objection, and the district court credited the response as adequate. The court adopted the factual statements in the PSR and found that it reasonably addressed the relevant conduct and accurately reported the applicable statutory sentences. In accordance with the Sentencing Guidelines, the court sentenced Midkiff to 168 months for the drug crimes and 360 months for the gun crimes, to run consecutively.[1]

II
Jackson argues that the district court erred when it denied his motion to suppress evidence found in and around his home during a search authorized by a state search warrant. He contends that the affidavit supporting the search warrant was based on incorrect and incomplete information, thus rendering the good-faith exception to the exclusionary rule inapplicable. He also argues that the search cannot be justified by the protective sweep rule because most of the evidence was found in the yard and not in the house itself.
We accept a district court's factual findings on a motion to suppress *240 based on live testimony at a suppression hearing "unless clearly erroneous or influenced by an incorrect view of the law." United States v. Foy, 28 F.3d 464, 474 (5th Cir.1994). When reviewing the district court's ruling, we will "view[] the facts in the light most favorable to the prevailing party." United States v. Howard, 106 F.3d 70, 73 (5th Cir.1997). Our review of the district court's interpretation and application of law is de novo. See United States v. Blocker, 104 F.3d 720, 725 (5th Cir.1997).
Although the parties' briefing primarily addresses the good-faith exception, our examination of the record does not indicate that the district court based its decision to deny Jackson's motion to suppress on the good-faith exception. Before ruling on the motion, the district court heard testimony from the officer who provided the affidavit supporting the search warrant and from one of the officers who conducted the search. After hearing argument from counsel, the district court stated:
[T]he ruling of the court is going to be [that] it's not a bare bones affidavit. But I think that if it were based on the affidavit alone, it would be suppressed. However, I do agree with the government in this particular case that the inevitable discovery doctrine works. I also think that you've got the independent source verification by the officer who sees the marijuana when he comes into the residence, and he was a different officer from Officer Ortiz, in any event. So I think those two doctrines allow this particular search, that the items seized to be admissible, and so the motion to suppress in this case will be overruled on that basis.
Based on this oral ruling, it is unclear whether the district court found that the good-faith exception applied.[2]
What is clear, however, is that the district court based its ruling at least in part on the inevitable discovery doctrine. Because of this alternate grounds for denying the motion to suppress, we do not reach the merits of the good-faith exception argument. Instead, we analyze the district court's determination that the evidence from the search of Jackson's home and the surrounding areas is admissible under the inevitable discovery doctrine. See United States v. Grosenheider, 200 F.3d 321, 327 (5th Cir.2000) (refusing to consider whether warrantless search was illegal because independent source doctrine applied); United States v. Register, 931 F.2d 308, 311 (5th Cir.1991) (refusing to consider whether exigent circumstances justified a warrantless entry because the independent source doctrine applied).[3]
*241 "The exclusionary rule of the Fourth Amendment generally prohibits the introduction at trial of not only primary evidence obtained as a direct result of an illegal search or seizure, but also evidence discovered later that is derivative of an illegality, or constitutes `fruit of a poisonous tree.'" Grosenheider, 200 F.3d at 327. "The primary limit on this rule is that otherwise suppressible evidence will still be admitted if the connection between the alleged illegality and the acquisition of the evidence is `so attenuated as to dissipate the taint.'" Id. (quoting Nardone v. United States, 308 U.S. 338, 341, 60 S.Ct. 266, 84 L.Ed. 307 (1939)). One example of this "attenuation" limit is known as the inevitable discovery doctrine, which renders the exclusionary rule inapplicable to otherwise suppressible evidence if that evidence would inevitably have been discovered by lawful means. See 5 WAYNE R. LAFAVE, SEARCH AND SEIZURE: A TREATISE ON THE FOURTH AMENDMENT § 11.4(a) (3d ed.1996).
The inevitable discovery rule applies if the Government demonstrates by a preponderance of the evidence that (1) there is a reasonable probability that the contested evidence would have been discovered by lawful means in the absence of police misconduct and (2) the Government was actively pursuing a substantial alternate line of investigation at the time of the constitutional violation. United States v. Lamas, 930 F.2d 1099, 1102 (5th Cir.1991).
It is undisputed that, even without the state search warrant, the federal arrest warrant gave the officers the authority to enter Jackson's residence to arrest him. See Payton v. New York, 445 U.S. 573, 603, 100 S.Ct. 1371, 63 L.Ed.2d 639 (1980) ("[A]n arrest warrant ... carries with it the limited authority to enter a dwelling in which the suspect lives when there is reason to believe the suspect is within."). Further, the officers had the authority to conduct a search of the area immediately surrounding the place where the arrest was made. See United States v. Virgil, 444 F.3d 447, 451 (5th Cir.2006) ("Any arrest may be accompanied by a search `incident to the arrest' of the immediate vicinity, limited to areas in which weapons might be found, regardless of probable cause or reasonable suspicion.") (quoting Maryland v. Buie, 494 U.S. 325, 334, 110 S.Ct. 1093, 108 L.Ed.2d 276 (1990)). Thus, the officers were acting within their authority when they discovered the bag of marijuana that Jackson had hidden under the couch when the officers came in. Our case law suggests that once the officers found the marijuana, probable cause existed to obtain a search warrant. United States v. Monroy, 614 F.2d 61, 64 (5th Cir.1980) ("The odor of marijuana provided probable cause for a wider search ...."); United States v. Melancon, 462 F.2d 82, 89 (5th Cir.1972) ("Probable cause is deemed to exist where the facts and circumstances within the affiant's knowledge ... are sufficient unto themselves to warrant a man of reasonable caution to believe that an offense has been or is being committed.") (internal quotation marks and citation omitted).
In addition to the marijuana, the officers found equipment and other materials *242 used in the manufacturing of methamphetamine outside the house. Because these items were located in the area surrounding the residence and the officers had authority to enter this area as they executed the arrest warrant, they could be seized pursuant to the plain view doctrine, which allows police to seize items without a search warrant. Such a warrantless seizure is permissible if: (1) the police lawfully entered the area where the item was located; (2) the item was in plain view; (3) the incriminating nature of the item was "immediately apparent;" and (4) the police had a lawful right of access to the item. United States v. Buchanan, 70 F.3d 818, 825-26 (5th Cir.1995) (citing Horton v. California, 496 U.S. 128, 136-37, 110 S.Ct. 2301, 110 L.Ed.2d 112 (1990)). Once seized, this evidence could not only be introduced at trial but also used as evidence of probable cause in support of a warrant. See United States v. Webster, 750 F.2d 307, 328 (5th Cir.1984).
In this case, the officers did not seek a search warrant based on the evidence which could have been seized pursuant to the arrest warrant because they already had a state search warrant. But, had they had reason to question the validity of the state search warrant or had there been no state search warrant, we have little doubt that the officers nonetheless could have secured a search warrant and conducted the search that yielded the disputed evidence.
As to the second requirement for invoking the inevitable discovery doctrine, it almost goes without saying that the government was actively pursuing a substantial alternate line of investigation at the time of the alleged constitutional violation. Lamas, 930 F.2d at 1102. Indeed, we have indicated that the "active-pursuit element" may no longer be necessary to invoke the inevitable discovery rule. Id. at 1104. In this case, we need not address the continuing vitality of the active-pursuit element, as an ongoing grand jury investigation that has already led to an indictment would clearly satisfy it.
Jackson's only argument addressing whether the evidence would have been inevitably discovered without the allegedly improper state search warrant focuses on the protective sweep that was conducted contemporaneously with the arrest. Jackson argues that the protective sweep could not legitimize the search because many of the seized items were found outside the house, and thus outside any area the police might reasonably have searched to ensure their safety. Regardless of the merits of this argument, there are, as discussed, other grounds supporting the application of the inevitable discovery doctrine. Jackson has waived any challenges to these other grounds by failing to address them in his briefing. See Goodman v. Harris County, 571 F.3d 388, 399 (5th Cir.2009) (noting that issues inadequately briefed on appeal are waived).
In conclusion, because the police would have inevitably discovered the evidence even had the state search warrant never issued, it need not be suppressed. The exclusionary rule is meant to put the police "in the same, not a worse, position than they would have been in if no police error or misconduct had occurred." Nix v. Williams, 467 U.S. 431, 443, 104 S.Ct. 2501, 81 L.Ed.2d 377 (1984). In this case, exclusion of the challenged evidence would put the police in a worse position than they would have been in absent the allegedly infirm state search warrant. Accordingly, we affirm the district court's denial of Jackson's motion to suppress the evidence on the basis of the inevitable discovery doctrine. We express no opinion as to whether the good-faith exception can be applied to the search.


*243 III
Midkiff presents two arguments on appeal. First, Midkiff contends that the district court erred in relying on the PSR's recommendations in making its sentencing determinations because the PSR relied on a quantity of drugs that had not been submitted to the jury and proved beyond a reasonable doubt in accordance with Apprendi v. New Jersey, 530 U.S. 466, 120 S.Ct. 2348, 147 L.Ed.2d 435 (2000). Second, Midkiff contends that his firearm-related convictions should be reversed because the district court impermissibly allowed the government to amend the indictment to conform the firearm serial number in the indictment to the serial number of the firearm introduced as evidence at trial.

A
On a special jury form, the jury found Midkiff and his co-conspirators guilty of conspiracy to distribute 50 grams or less of methamphetamine, but not guilty of conspiracy to distribute 50 to 500 grams or 500 grams or more. Nonetheless, the Probation Officer attributed 1,318 grams of methamphetamine to Midkiff based on extrapolation from estimates provided by co-conspirators. This increased Midkiff's base offense level by at least eight. See U.S.S.G. § 2D1.1(c). Midkiff objected to the PSR "in its entirety," but did not specifically object to the amount of methamphetamine attributed to him. He now argues that the entire PSR was tainted by the preparer's subjective belief, which conflicted with the unanimous findings of the jury regarding drug quantity.
It is unnecessary to decide whether to apply our typical standard of review or plain error review because both our precedent and Supreme Court precedent foreclose Midkiff's argument regardless of the standard we apply. We have held that a "district court correctly calculated the quantity of drugs [for sentencing purposes] notwithstanding the fact that the jury specifically acquitted [the defendant] of the large drug quantities later found by the judge." United States v. Pineiro, 470 F.3d 200, 206 (5th Cir.2006) (quotations omitted). Likewise, the Supreme Court has held that "a jury's verdict of acquittal does not prevent the sentencing court from considering conduct underlying the acquitted charge [in sentencing], so long as that conduct has been proved by a preponderance of the evidence." United States v. Watts, 519 U.S. 148, 157, 117 S.Ct. 633, 136 L.Ed.2d 554 (1997).[4] In this case, the jury simply found that the government had not proved the larger quantities beyond a reasonable doubt. The acquittal sheds no light on whether a preponderance of the evidence established the larger quantities, and Midkiff has not argued that the preponderance of the evidence standard was not met.
"In making its factual findings for sentencing, a district court may adopt the findings of the PSR without additional inquiry if those facts have an evidentiary basis with sufficient indicia of reliability and the defendant does not present rebuttal evidence or otherwise demonstrate that the information is materially unreliable." United States v. Ford, 558 F.3d 371, 377 (5th Cir.2009). In this case, the quantity of methamphetamine attributed to Midkiff has an evidentiary basis with sufficient indicia of reliability. The PSR notes that one of Midkiff's co-conspirators, Jesse Wayne Williams, advised in an interview with police that he had "cooked" 3/4 of an *244 ounce to 1 ounce (21.26 grams to 28.35 grams) of methamphetamine once or twice each day over a period of two weeks before his arrest. Utilizing the minimum estimates provided by Williams, the PSR calculated the amount of methamphetamine cooked over this period as 298 grams. Similarly, Williams estimated that in the six-month period prior to that time, he had cooked 3/4 of an ounce to 1 ounce two to four times a week, resulting in a total estimated quantity for that time period of 1,020 grams. The 1,318 gram total utilized by the probation officer reflects the 298 grams produced in the two weeks prior to arrest and the 1,020 grams produced previously. The PSR details information gathered not just from Williams, but from law enforcement witnesses who testified regarding traffic stops, surveillance, and other seizures of evidence, and from multiple co-conspirators who provided information regarding Williams' role as a methamphetamine cook for the conspiracy. The PSR further notes that this information was corroborated through a review of grand jury and trial transcripts. Based on the foregoing, we conclude that the quantities set forth in the PSR were reasonable, extrapolated estimates supported by sufficient indicia of reliability. See United States v. Valdez, 453 F.3d 252, 267 (5th Cir.2006).
Finally, we note that Midkiff's sentence of 168 months imprisonment on the drug conspiracy count is less than the maximum sentence authorized by the jury's verdict.[5] We have previously found no Apprendi error where a district court determined the quantity of drugs under the preponderance of the evidence standard and sentenced the defendant to a term of imprisonment within the statutory range authorized by the jury's verdict. See United States v. Doggett, 230 F.3d 160, 165 (5th Cir.2000).

B
Midkiff also argues that his convictions for possession of a firearm in furtherance of a drug trafficking crime and possession of a firearm by a convicted felon should be reversed because the serial number provided in the indictment for the firearm at issue was not the same as the serial number for the firearm introduced as evidence at trial. He argues that the district court erred by permitting an amendment to the indictment after the close of all evidence, particularly when the government had knowledge of the discrepancy early in the trial, if not earlier, and failed to move to amend until evidence was closed.
Generally, indictments can only be amended by a grand jury. United States v. Adams, 778 F.2d 1117, 1122, 1125 (5th Cir.1985). But, "[t]he form of an indictment may be amended without return to the grand jury so long as its substance remains the same," such as by correcting a "misnomer" or mistake of form. United States v. Young Bros., Inc., 728 F.2d 682, 693 (5th Cir.1984). Thus, the issue is whether the amendment to the serial number constituted a change in form akin to correcting a typographical error or a change in substance that impermissibly altered the indictment.
Although we have never addressed this question directly, precedent from this circuit and others suggests that the particular attributes of a firearm are not actual elements of the offense. See, e.g., United States v. Munoz, 150 F.3d 401, 417 (5th Cir.1998) (finding no grounds to reverse conviction when indictment charged a different *245 gauge of shotgun than that presented during trial); United States v. Robinson, 974 F.2d 575, 578 (5th Cir.1992) (holding that "when an indictment alleges non-essential facts, the government need not prove them in order to sustain a conviction"); United States v. Robison, 904 F.2d 365, 369 (6th Cir.1990) (noting that "the specific type of firearm used or possessed... is not an essential element of [a § 924(c) violation]"); see also United States v. Morrow, 925 F.2d 779, 781 (4th Cir.1991) (affirming district court finding that a one-digit difference between serial number of firearm as stated in indictment and the firearm presented at trial to be a typographical error that went to form, not substance, of indictment); United States v. Neff, 525 F.2d 361, 363 (8th Cir.1975) (same). These cases support a conclusion that the change was one of form, not substance, and thus permissible.
We also have noted that "[a]n amendment will be allowed if a defendant's rights are not affected and he is adequately apprised of the charges against him so that he is protected against surprise at trial...." Young Bros., 728 F.2d at 693. In this case, Midkiff has not contended that he was prejudiced either by the amendment itself, or by the district court's decision to permit the amendment after the government had rested. He does not claim that he was surprised by the trial evidence, or that his ability to defend the charges was impaired in any way. Given that Midkiff has neither alleged nor shown prejudice, we find no abuse of discretion in the district court's decision to allow the government to reopen its case to amend the indictment. See United States v. Molinares, 700 F.2d 647, 652 (11th Cir.1983) (finding that the court of appeals "will not disturb the district court's exercise of discretion [to re-open a case] unless the circumstances of the case show that [the defendant] suffered actual prejudice in the conduct of his defense") (citing United States v. Marino, 562 F.2d 941, 944 (5th Cir.1977)); Maggard v. Wainwright, 432 F.2d 941, 942 (5th Cir.1970) (noting that trial courts are vested with considerable discretion in deciding whether to allow a party to re-open its case).

IV
In conclusion, we find the appellants' arguments unavailing and affirm the convictions. We also find no error in Midkiff's sentence.
AFFIRMED.
NOTES
[1]  Because Jackson does not challenge his sentence, we limit our discussion of sentencing to Midkiff.
[2]  On the one hand, a determination that the affidavit is more than "bare bones" is relevant to determining good faith. See United States v. Cisneros, 112 F.3d 1272, 1278 (5th Cir. 1997) ("An officer may rely in good faith on the validity of a warrant so long as the warrant is supported by more than a bare bones affidavit.") (citation and internal quotation marks omitted). On the other, the court states that the affidavit alone cannot support the search and makes no finding regarding Jackson's argument that the affidavit was misleading and contained false information. See Franks v. Delaware, 438 U.S. 154, 171-72, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978) (noting that when defendant has made the requisite showing as to falsehood in the affidavit, the court should set to one side the questionable material, and then determine if there remains sufficient content in the warrant affidavit to support a finding of probable cause); United States v. Sibley, 448 F.3d 754, 757 (5th Cir. 2006) (noting that the good-faith exception does not apply when the magistrate issuing the warrant was misled by information in an affidavit that the affiant knew or should have known was false).
[3]  The independent source doctrine cases are applicable in this context because the two doctrines "are actually two sides of the same coin." Grosenheider, 200 F.3d at 328. The Supreme Court has treated inevitable discovery as "an extrapolation" of the independent source doctrine. See Murray v. United States, 487 U.S. 533, 539, 108 S.Ct. 2529, 101 L.Ed.2d 472 (1988) ("Since the tainted evidence would be admissible if in fact discovered through an independent source, it should be admissible if it inevitably would have been discovered.") (emphasis omitted); see also 5 WAYNE R. LaFAVE, SEARCH AND SEIZURE: A TREATISE ON THE FOURTH AMENDMENT § 11.4(a) (3d ed.1996) (referring to inevitable discovery as "a variation" on the independent source doctrine).
[4]  We previously have held that Watts remains valid after United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). See United States v. Farias, 469 F.3d 393, 399 (5th Cir.2006).
[5]  Because on his prior felony drug conviction, Midkiff was subject to an enhanced penalty of 30 years imprisonment on the conspiracy charge. See 21 U.S.C. § 841(b)(1)(C).
