 United States Court of Appeals
         FOR THE DISTRICT OF COLUMBIA CIRCUIT



Argued September 12, 2016          Decided November 15, 2016

                        No. 15-3051

                UNITED STATES OF AMERICA,
                        APPELLEE

                              v.

                   KEVIN EUGENE MACK,
                       APPELLANT


        Appeal from the United States District Court
                for the District of Columbia
                   (No. 1:13-cr-00150-1)


     John A. Briley, Jr. argued the cause and filed the briefs
for appellant.

    Karen P. Seifert, Assistant U.S. Attorney, argued the
cause for appellee. With her on the brief was Elizabeth
Trosman, Assistant U.S. Attorney. Lauren R. Bates, Assistant
U.S. Attorney, entered an appearance.

    Before: BROWN, Circuit Judge, and EDWARDS and
GINSBURG, Senior Circuit Judges.

   Opinion for the Court filed by Senior Circuit Judge
EDWARDS.
                               2
     EDWARDS, Senior Circuit Judge: On May 23, 2013,
appellant Kevin Mack was charged by indictment with two
counts of distribution of a mixture or substance containing
phencyclidine (PCP), in violation of 21 U.S.C. § 841(a)(1),
(b)(1)(B)(iv), (b)(1)(C), for twice selling PCP to an
undercover police officer. On July 21, 2014, appellant pled
guilty to one count of the indictment. On July 28, 2015, the
District Court imposed a 77-month term of incarceration and
36 months of supervised release. In his appeal to this court,
appellant contends that the District Court erred by failing to
consider his arguments for a time-served sentence. In
particular, appellant claims that the trial judge ignored his
“sentencing manipulation” argument – i.e., that the
undercover officer arranged the second PCP sale solely to
increase his sentence. Appellant also argues that the District
Court erred in calculating the quantity of PCP attributable to
him.

     At the time of sentencing, a district court judge is
required to state in open court the reasons for choosing a
particular sentence. 18 U.S.C. § 3553(c) (2012). This
requirement has been construed to mean that the trial judge
must address all “nonfrivolous reasons” for an alternative
sentence asserted by a defendant and provide a “reasoned
basis” in open court for any sentencing decision. United
States v. Locke, 664 F.3d 353, 357 (D.C. Cir. 2011) (quoting
Rita v. United States, 551 U.S. 338, 356–57 (2007)).

     The trial judge in this case expressly rejected appellant’s
claim that he had been “induced” by police officers to engage
in unlawful conduct in an order denying appellant’s motion to
dismiss the indictment. But the trial judge did not explicitly
address the issue of “sentencing manipulation” when he
rendered his sentencing decision. However, after explaining
the reasons for his sentencing decision, the trial judge asked
                              3
appellant’s counsel on two occasions whether there was any
reason why the court should not impose the sentence on the
terms indicated. Counsel said “no.” In other words, even
when afforded the opportunity to object, defense counsel
never complained that the trial judge had failed to address
appellant’s sentencing manipulation argument. In these
circumstances, we hold that appellant did not preserve his
claim that the District Court failed to adequately address his
sentencing manipulation argument. We therefore review this
claim for plain error. On the record before us, we find no
plain error affecting appellant’s substantial rights.

    We also hold that the District Court did not clearly err in
calculating the quantity of the liquids containing PCP that
were the subject of the drug transactions. Under the clearly
erroneous standard, the District Court’s findings of fact are
presumptively correct. In re Sealed Case, 552 F.3d 841, 844
(D.C. Cir. 2009). On the record before us, we find no basis to
overcome this presumption.

                    I. BACKGROUND

A. Summary of the Facts

     In 2012, the Metropolitan Police Department (“MPD”)
was investigating the sale of PCP in the District of Columbia.
That investigation led an undercover MPD officer to contact
someone named “Rico,” who steered the officer to his “Uncle
Jimmy,” claiming that Jimmy was Rico’s PCP supplier. After
failed attempts to contact Jimmy by telephone, appellant
Kevin Mack texted the undercover officer and arranged to sell
him PCP. On July 23, 2012, appellant sold six vials of liquid
PCP to the undercover officer for $1,200. The transaction was
video-recorded. A sample of the liquid was submitted to the
                              4
Drug Enforcement Administration (“DEA”) for analysis and
determined to be PCP with a purity of 4.9%.

     Appellant and the undercover officer continued to
exchange text messages after the first sale. They arranged
another sale about a week after their first exchange, but when
the MPD officer arrived at the second buy, appellant reported
that he did not have the PCP prepared for delivery. A month
later, appellant and the undercover officer arranged another
meeting. On September 5, 2012, appellant sold six vials of
liquid PCP to the undercover officer for $1,800. This
transaction was also video-recorded. DEA later determined
from a sample of the liquid that it was PCP with a purity of
6.7%.

    For several months after the second PCP transaction,
MPD deliberated over how to proceed with its investigation.
Because the lead officer involved in appellant’s case became
involved in a different matter, MPD decided to close the case
and proceed with prosecution. On May 23, 2013, a grand jury
charged appellant with one count of unlawful distribution of a
mixture or substance containing PCP, and one count of
unlawful distribution of one hundred grams or more of a
mixture or substance containing PCP, in violation of 21
U.S.C. § 841(a)(1), (b)(1)(B)(iv), (b)(1)(C).

B. The Proceedings Before the District Court

     On April 30, 2014 and May 31, 2014, appellant filed
motions to dismiss on the grounds of entrapment and selective
prosecution. The District Court denied these motions. United
States v. Mack, 53 F. Supp. 3d 179 (D.D.C. 2014). The court
ruled that no government agents “engaged in persuasive
overtures” in soliciting appellant, “beyond those ordinarily
present in drug transactions.” Id. at 188. The court also found
                               5
that the government “did not solicit the Defendant directly,”
and noted that the first sale “was initiated by the Defendant . .
. out of his own volition.” Id. Regarding the second PCP sale,
the court noted that, although it “resulted from a series of text
messages between the undercover officers and the
Defendant,” there was “no evidence” of “persuasive
overtures” by MPD officers or “any reluctance” on the part of
appellant. Id. The court additionally found that appellant had
not provided any “factual predicate or evidentiary foundation”
for his entrapment argument. Id.

     Finally, the court rejected appellant’s claim of selective
prosecution. On this claim, the court found that appellant had
“not put forth a shred of evidence even hinting at the
existence of a discriminatory purpose behind the decision to
prosecute him.” Id.

     On July 21, 2014, appellant entered a guilty plea to Count
One of the indictment. The plea agreement provided that the
parties’ dispute over the drug quantity with respect to the
relevant conduct would be resolved by the court as part of the
sentencing procedures.

    1.   The Drug Quantity Hearing

     Before sentencing, the District Court held a hearing at
which the prosecution offered evidence to support its
calculation that the relevant drug quantity was 222 grams. The
Government’s Brief to this court accurately describes the
testimony and evidence that was received by the District
Court:

       Officer Cardinal . . . stated that liquid PCP has
    a “distinct chemical odor,” typically a yellow or
    amber tint, and often contains engine starter fluid.
                           6
[He] explained [that when] . . . more than one
ounce is obtained by MPD, it uses a process called
“remediation” wherein it submits only one ounce
from the larger sample to DEA. First, each separate
vial is weighed on a calibrated scale. Next, each
vial is tested with a field-test kit to determine if it
has a reaction for PCP. Thereafter, the liquid in all
the vials is emptied into a beaker and weighed
together. The weight of the beaker is subtracted
from that amount to get the weight of the liquid
substance. Finally, a one-ounce sample is taken
from the liquid mixture and sent to DEA. The
remaining substance is sent to MPD’s evidence
collection division for destruction. MPD officers
document all of these steps with photographs.
Officer Cardinal testified that he takes these steps
because DEA [will] . . . only receive a maximum
of one ounce of liquid PCP, due to its volatility.
    ....

    Regarding the transaction on July 23, 2012,
Officer Cardinal introduced photographs showing
the four half-ounce vials and two one ounce vials
that the undercover officer had purchased from
appellant, the positive field tests for PCP from
each vial, and the other steps in the remediation
process. All six vials contained liquid that was
consistent in odor and color with liquid PCP. The
Officer testified that the liquid PCP purchased
from appellant on July 23 weighed 87.6 grams,
without any packaging. One ounce (25.4 grams)
was sampled from this mixture, secured in
appropriate packaging, and sent to DEA’s Mid-
Atlantic Laboratory. That sample was tested by
                               7
    DEA and shown to contain PCP, with a 4.9%
    purity.

        Regarding the transaction on September 5,
    2012, Officer Cardinal introduced photographs
    showing the six one-ounce vials that the
    undercover officer had purchased from appellant,
    the positive field tests for PCP from each vial, and
    the other steps in the remediation process. All six
    vials contained liquid that was consistent in odor
    and color with liquid PCP. The Officer testified
    that the liquid PCP purchased on September 5
    weighed 133.4 grams, without any packaging. One
    ounce (25.1 grams) was sampled from this
    mixture, secured in appropriate packaging, and
    sent to DEA’s Mid-Atlantic Laboratory. That
    sample was tested by DEA and shown to contain
    PCP, with a 6.7% purity.

        Investigator Derek Starliper testified that he
    was part of the team that secured the liquid PCP
    purchased from appellant. . . . [H]e took physical
    custody of the vials from the undercover officer,
    packaged and labeled them, deposited them into
    the MPD evidence room, retrieved them for
    remediation by Officer Cardinal, and then
    submitted the sample produced from the
    remediation process to DEA.

Br. for Appellee 6–9 (citations omitted).

     Appellant offered no evidence at the hearing. Instead,
appellant submitted a Memorandum in which he questioned
the reliability of the measurements and field tests conducted
by MPD; argued that only the amount of drugs actually
                              8
measured and tested by DEA should be used to calculate the
relevant drug quantity; and also argued that the alleged weight
of the liquid PCP from the second transaction should not be
included in the relevant drug quantity because the DEA
chemist did not testify at the hearing.

     On May 14, 2015, the District Court issued an order
finding that MPD “followed sufficiently reliable procedures
when they handled and measured the weight of the drug
evidence” and proved the relevant drug quantity beyond a
preponderance of the evidence. Memorandum & Order at 10–
11, United States v. Mack, No. 13-cr-0150 (D.D.C. May 14,
2015), Supplemental Appendix (“S.A.”) 57–58. The District
Court found no merit in appellant’s argument that the court
should consider only the drug quantity sent to DEA. Id. at 8–
9, S.A. 55–56. The court pointed out that drug sampling
procedures that were followed in this case were approved in
United States v. Sheffield, 842 F. Supp. 2d 227, 228–29 & n.2
(D.D.C. 2012), as well as United States v. McCutchen, 992
F.2d 22 (3d Cir. 1993), and United States v. Self, 681 F.3d
190 (3d Cir. 2012). Id. at 8–9, S.A. 55–56.

    2.   The Sentencing Hearing

    Prior to sentencing, appellant filed a Memorandum
requesting a “time-served” sentence. Appellant argued that he
had been convicted in Maryland and was likely to be
imprisoned there for five years or more; he was selectively
prosecuted; he was solicited by police and the September 5,
2012, transaction was engineered to increase the drug quantity
amount; and he was inappropriately prosecuted in federal
court instead of D.C. Superior Court. Appellant also
submitted separate written objections to the calculation of his
Sentencing Guidelines range in the Presentence Report, again
                               9
asserting that the court should consider only the drug quantity
sent to DEA.

     During the sentencing hearing, the District Court listened
to arguments from appellant’s counsel and the prosecutor.
The prosecutor explained to the court that appellant had not
been selectively prosecuted, but rather that there was not
sufficient evidence to proceed against other parties. The
District Court addressed this point in noting that “many of the
individuals caught up in the PCP investigation that resulted in
the instant matter did not face justice.” Tr. of Sentencing
Hearing at 23, S.A. 159. The District Court also addressed
appellant’s argument that he was arbitrarily prosecuted in
federal court. The trial judge asked the prosecutor: “[I]n this
particular case, what [were] the driving factors that resulted in
it being brought here rather than in superior court?” Id. at 15,
S.A. 151. The prosecutor pointed to the amount of drugs and
appellant’s criminal history. Id. at 15–16, S.A. 151–52.

     The District Court imposed a 77-month term of
incarceration and 36 months of supervised release, which
would run concurrently with any sentence appellant served in
his Maryland case. The court reviewed the sentencing factors
in 18 U.S.C. § 3553(a), noting that the offense was “serious,
PCP is a tremendously dangerous and destructive substance”
and discussing appellant’s “tremendously long criminal
history,” which included “repeated criminal convictions,”
showing “that he is not easily deterred.” Tr. of Sentencing
Hearing at 23, S.A. 159. The court also stated that appellant
had been unsuccessful on repeated attempts at supervised
release. The court rejected appellant’s request for a time-
served sentenced because appellant had appealed his
Maryland case and the court needed to “ensure[] the public’s
protection” if appellant was successful in that appeal. Id. at
24, S.A. 160.
                             10

     There is nothing in the record, however, to indicate that
the trial judge addressed appellant’s sentencing manipulation
argument during the sentencing hearing. Appellant raised this
claim in his written Memorandum before sentencing and
again during defense counsel’s oral presentation at
sentencing. But the trial judge never explicitly commented on
appellant’s request for mitigation on the ground of sentencing
manipulation.

     Although the trial judge did not expressly address
sentencing manipulation during the course of sentencing,
defense counsel declined two opportunities to object to the
sentencing judge’s statement of reasons. After reciting his
statement of reasons for appellant’s sentence, the trial judge
said:

     I will now indicate the sentence to be imposed, but
     counsel will have one more opportunity to make
     any legal objections on the factors I have considered
     before I impose the sentence. Any further legal
     objections?

Id. at 25, S.A. 161. Defense counsel replied “[n]o, Your
Honor.” Id. Then, after announcing appellant’s sentence and
explaining the terms of his supervised release, the District
Court again asked “Counsel, any reason that I should not
impose the sentence other than those previously argued as just
stated?” and defense counsel replied “[n]o, Your Honor.” Id.
at 27–28, S.A. 163–64.
                              11
                      II. ANALYSIS

A. Standard of Review 

     Following the Supreme Court’s decisions in United
States v. Booker, 543 U.S. 220 (2005), and Gall v. United
States, 552 U.S. 38 (2007), appellate courts review sentences
under an abuse-of-discretion standard and set aside sentences
found to be “unreasonable.” Booker, 543 U.S. at 261–63;
Gall, 552 U.S. at 51.

     This review proceeds in two steps. First, the appellate
court must “ensure that the district court committed no
significant procedural error, such as failing to calculate (or
improperly calculating) the Guidelines range, treating the
Guidelines as mandatory, failing to consider the § 3553(a)
factors, selecting a sentence based on clearly erroneous facts,
or failing to adequately explain the chosen sentence—
including an explanation for any deviation from the
Guidelines range.” Gall, 552 U.S. at 51. “In applying the
clearly erroneous standard, an appellate court must remain
mindful that judicial findings of fact are presumptively
correct.” In re Sealed Case, 552 F.3d at 844 (citations and
internal quotation marks omitted). Second, the appellate court
reviews the substantive reasonableness of the sentence under
an abuse-of-discretion standard. Id.; see also United States v.
Gardellini, 545 F.3d 1089, 1092–93 & n.2 (D.C. Cir. 2008).
This case involves only the first step.

     When a party fails to preserve a procedural challenge to
his sentence, we review for plain error. See Locke, 664 F.3d at
357 (“The more demanding plain error standard of review
applies where a defendant fails to raise a claim at his
sentencing hearing or fails to object to a district court's
ruling.”); United States v. Akhigbe, 642 F.3d 1078, 1085
                               12
(D.C. Cir. 2011) (“[O]ur review is for plain error because . . .
[the defendant] failed in the district court to object to the
adequacy of that court's reasoning.”).

     “To overturn a district court's decision under plain error
review, we must find that there is (1) error, (2) that is plain,
and (3) that affects substantial rights. If all three conditions
are satisfied, we have discretion to remedy the error only if
(4) it seriously affects the fairness, integrity, or public
reputation of judicial proceedings.” United States v. Baldwin,
563 F.3d 490, 491 (D.C. Cir. 2009) (citations, brackets, and
internal quotation marks omitted). To affect substantial rights,
the defendant must “show a reasonable probability that, but
for the error, the outcome of the proceeding would have been
different.” Molina-Martinez v. United States, 136 S. Ct. 1338,
1343 (2016) (citation and internal quotation marks omitted).

B. Appellant’s Procedural Challenges

     As noted above, a district court judge must “state in open
court the reasons for its imposition of the particular sentence.”
18 U.S.C. § 3553(c) (2012). The sentencing judge “must
adequately explain the chosen sentence to allow for
meaningful appellate review and to promote the perception of
fair sentencing.” Gall, 552 U.S. at 50. The judge need not
recite “a full opinion in every case,” and the length and depth
of the judge’s explanation “depends upon circumstances.”
Rita, 551 U.S. at 356. The guiding principle is that “[t]he
sentencing judge should set forth enough to satisfy the
appellate court that he has considered the parties’ arguments
and has a reasoned basis for exercising his own legal
decisionmaking authority.” Id.

    Part of the sentencing judge’s obligation under 3553(c) is
to respond to a defendant’s “nonfrivolous reasons for
                               13
imposing a different sentence.” Id. at 357. When a defendant
advances nonfrivolous arguments, “the judge will normally go
further and explain why he has rejected those arguments.” Id.
If the sentencing judge gives such an explanation, “we
generally presume that he adequately considered the
arguments and will uphold the sentence if it is otherwise
reasonable.” Locke, 664 F.3d at 358. By contrast, if the
sentencing judge fails to respond to a nonfrivolous argument,
the presumption of adequate consideration is rebutted. See
United States v. Bigley, 786 F.3d 11, 14 (D.C. Cir. 2015).

     Appellant argues that “the record of the sentencing
procedures includes no explanation by the district judge for
not agreeing with, or even considering” several of his
arguments for a below-Guidelines sentence. Br. for Appellant
9. Specifically, appellant claims that the District Court did not
consider the arguments that he was “selectively prosecuted,”
that he was arbitrarily prosecuted in federal court (and not
state court), and that the officers “solicited a second PCP
transaction, in order to enlarge the guideline sentencing
range.” Id. at 8.

     The record largely contradicts those assertions. As
discussed in detail in the Background section, the trial judge
afforded appellant ample opportunities to air his concerns
about sentencing; he explicitly addressed appellant’s selective
and arbitrary prosecution arguments; he sought clarifications
and explanations from the prosecutor; and he offered a
carefully reasoned judgment for his sentencing decision. The
judge’s only omission was his failure to explicitly address
appellant’s sentencing manipulation claim.

    Prior to our 2015 decision in Bigley, there was
uncertainty in our Circuit about whether sentencing
manipulation was even a plausible argument for a reduced
                               14
sentence. See United States v. Oliveras, 359 Fed. App’x 257,
261 n.5 (2d Cir. 2010) (summary order) (“Our sister Circuits
have adopted widely different positions on the availability of
the sentencing manipulation and sentencing entrapment
doctrines. . . . [T]he D.C. Circuit has strongly suggested that it
would not recognize either doctrine.”). However, as we
explained in United States v. McKeever, 824 F.3d 1113, 1123
(D.C. Cir. 2016), the “law of the circuit is now clear that a
defendant may raise a mitigation argument resting on
sentencing entrapment to request a downward variance in his
sentence.”

     “Sentencing manipulation occurs when the government
unfairly exaggerates the defendant's sentencing range by
engaging in a longer-than-needed investigation and, thus,
increasing the drug quantities for which the defendant is
responsible.” United States v. Torres, 563 F.3d 731, 734 (8th
Cir. 2009); see also Bigley, 786 F.3d at 15 (recognizing
sentencing manipulation where an “officer ma[de] multiple
drug buys from the defendant before finally arresting him”).
In slight contrast, sentencing entrapment occurs “if the
government induces a defendant to commit a more serious
crime when he was predisposed to commit a less serious
offense.” United States v. Walls, 70 F.3d 1323, 1329 (D.C.
Cir. 1995). We have recognized both sentencing manipulation
and sentencing entrapment, and a district court is obligated
under 3553(c) and Rita to respond to those arguments. Bigley,
786 F.3d at 14 (“When a district court confronts a
nonfrivolous argument for a sentence below the relevant
guideline range, it must consider it.” (citing Locke, 664 F.3d
at 357)).

    In this case, defense counsel advanced a sentencing
manipulation argument, albeit with little clarity. It would have
helped if counsel had cited Bigley, which was published
                             15
before appellant’s sentencing proceeding, and before defense
counsel filed his Memorandum in Aid of Sentencing.
Nevertheless, counsel did raise a vaguely discernable
sentencing manipulation argument in writing and orally.

     In his written Memorandum, defense counsel argued that
“‘time served’ would be an appropriate sentence” because,
among other reasons, “the second transaction (on 9/05/12) has
served no other purpose than to enhance the drug quantity
amount on which the Court will base its sentence.”
Defendant’s Memorandum in Aid of Sentencing 3–4 (June
26, 2015), Appendix for Appellant 21–22. At the sentencing
hearing, defense counsel argued further that

    Mr. Mack was, for lack of a better term, lured into a
    second transaction and the net result of that
    transaction, it didn’t further the investigation, it
    didn’t result in any major breakthrough for the law
    enforcement. All it did was put Mr. Mack in a
    position of having a greater sentence than if he had
    been arrested within a short time following his first
    offense . . . .

Tr. of Sentencing Hearing at 12, S.A. 148. And on appeal,
defense counsel again alleged that “the MPDC officers had
solicited a second PCP transaction, in order to enlarge the
guideline sentencing range.” Br. for Appellant 8.
Nevertheless, the transcript of the sentencing hearing shows
that the District Court did not recognize or consider this
argument at sentencing.

    Prior to sentencing, the District Court gave careful
consideration to an argument closely related to appellant’s
sentencing manipulation argument. In defense counsel’s
motion to dismiss the indictment, counsel argued that the
undercover officers “induced the defendant’s participation in
                              16
the PCP-for-money transaction on September 5, 2012 for the
sole purpose of exposing the defendant to additional penal
sanctions.” Omnibus Motion to Dismiss Indictment; to
Compel Discovery; For a Severance of Counts; and, For a Bill
of Particulars at 2, United States v. Mack, No. 13-cr-0150
(D.D.C. May 31, 2014). The District Court rejected this
argument in a published opinion denying the motion to
dismiss. Mack, 53 F. Supp. 3d 179. The court found that

    the second drug sale, which resulted from a series of
    text messages between the undercover officers and
    the Defendant, does not amount to inducement as
    there is no evidence that the Government's requests
    were accompanied by persuasive overtures or that
    the Defendant displayed any reluctance in
    consummating the transaction. The Defendant has
    not provided the factual predicate or evidentiary
    foundation necessary to meet his initial burden of
    showing government inducement.

Id. at 188 (citation omitted). The defendant’s sentencing
manipulation claim is essentially identical to his inducement
claim: both allege that MPD officers improperly induced the
second drug sale.

     Of course, the District Court’s prior consideration of
appellant’s sentencing manipulation argument is not a perfect
substitute for explicit recognition at the sentencing proceeding
itself. We have previously explained that sentencing judges
“must adequately explain the chosen sentence . . . not only for
the defendant but also for the public to learn why the
defendant received a particular sentence.” In re Sealed Case,
527 F.3d 188, 193 (D.C. Cir. 2008) (citation and internal
quotation marks omitted). Prior consideration of an argument
in an earlier written opinion does less to adequately explain a
                              17
particular sentence than an explanation during the sentencing
proceeding itself. However, the District Court’s prior written
opinion at least confirms that the court considered all of the
“nonfrivolous reasons” asserted for a lesser sentence. Rita,
551 U.S. at 357. Indeed, the record reveals that the trial judge
was consistently attentive to the concerns raised by appellant.
And there is more to be taken into account with respect to the
trial judge’s handling of sentencing.

     In Locke, we stressed the importance of affording a
defendant an “opportunity to object to the district court’s
sentencing determination at sentencing.” 664 F.3d at 357.
There is no claim here that appellant was denied an
opportunity to pursue his sentencing manipulation claim at
sentencing. It is unclear why defense counsel failed to raise an
objection when the District Court never mentioned appellant’s
sentencing manipulation argument. It may be that counsel
recalled the judge’s opinion denying appellant’s motion to
dismiss, in which the court rejected appellant’s claim that he
had been “induced” by police officers to engage in the
unlawful drug sales. Counsel may have decided that it would
be fruitless to raise even a variation of the “inducement”
argument again. In any event, it is clear that defense counsel
did not object when the trial judge set forth the reasons
supporting the sentencing decision without explicit reference
to sentencing manipulation.

    The alleged error raised by appellant in this appeal is the
District Court’s failure to address his sentencing manipulation
argument at sentencing. However, that alleged error was
muted when the trial judge asked defense counsel near the
conclusion of sentencing whether he had “[a]ny further legal
objections[.]” Tr. of Sentencing Hearing at 25, S.A. 161. In
other words, before rendering his final judgment on
sentencing, the trial judge essentially asked defense counsel
                              18
“have I missed anything?” And the judge queried defense
counsel twice, and each time counsel said “No, Your Honor.”
Any protest of the alleged error was therefore forfeited.

    When a defendant fails to raise objections at sentencing,
we review only for plain error. United States v. Warren, 700
F.3d 528, 531 (D.C. Cir. 2012). As the Supreme Court has
explained, there are good reasons for this rule:

         If a litigant believes that an error has occurred
     (to his detriment) during a federal judicial
     proceeding, he must object in order to preserve the
     issue. If he fails to do so in a timely manner, his
     claim for relief from the error is forfeited. No
     procedural principle is more familiar to this Court
     than that a . . . right may be forfeited in criminal as
     well as civil cases by the failure to make timely
     assertion of the right before a tribunal having
     jurisdiction to determine it.

       ....

         This limitation on appellate-court authority
     serves to induce the timely raising of claims and
     objections, which gives the district court the
     opportunity to consider and resolve them. That
     court is ordinarily in the best position to determine
     the relevant facts and adjudicate the dispute. In the
     case of an actual or invited procedural error, the
     district court can often correct or avoid the mistake
     so that it cannot possibly affect the ultimate
     outcome. And of course the contemporaneous-
     objection rule prevents a litigant from
     “sandbagging” the court—remaining silent about
                              19
     his objection and belatedly raising the error only if
     the case does not conclude in his favor.

         In federal criminal cases, Rule 51(b) tells parties
     how to preserve claims of error: “by informing the
     court—when the court ruling or order is made or
     sought—of the action the party wishes the court to
     take, or the party's objection to the court's action
     and the grounds for that objection.” Failure to abide
     by this contemporaneous-objection rule ordinarily
     precludes the raising on appeal of the unpreserved
     claim of trial error. Rule 52(b), however, recognizes
     a limited exception to that preclusion. The Rule
     provides, in full: “A plain error that affects
     substantial rights may be considered even though it
     was not brought to the court's attention.”

Puckett v. United States, 556 U.S. 129, 134–35 (2009)
(citations and internal quotation marks omitted).

      On the record before us, we can find no basis upon which
to overturn the judgment of the District Court. The trial judge
gave appellant’s counsel two opportunities to contest the
proposed sentencing decision before sentence was
pronounced. Trial judges often are pressed with a long litany
of claims during sentencing, so it may happen that a judge
inadvertently fails to address a claim that a defendant believes
to be of consequence. In these circumstances, if a trial judge –
as in this case – asks defense counsel whether there are any
further objections to sentencing, it is incumbent upon counsel
to voice any concerns regarding matters that counsel believes
have not been addressed by the judge. As the Supreme Court
said in Puckett, this contemporaneous-objection rule prevents
a litigant from “sandbagging” the trial judge.
                               20
    Because appellant forfeited his objection that the trial
judge erred in failing to address his sentencing manipulation
argument, we review the objection pursuant to the plain error
standard. As the Supreme Court makes clear in Puckett, plain
error review does not mean that a defendant cannot prevail on
a challenge to a sentencing decision. See, e.g., United States v.
Brown, 808 F.3d 865 (D.C. Cir. 2015) (vacating a sentence
and remanding for resentencing because the appellate court
was unable to discern the sentencing judge’s rationale for
imposing an above-Guidelines sentence); United States v.
Burroughs, 613 F.3d 233 (D.C. Cir. 2010) (vacating a plainly
erroneous condition of supervised release). Plain error review
simply means that the standard of review is very stringent and
the likelihood of prevailing on appeal is greatly diminished. In
applying Rule 52(b), we will vacate a plain error only if it
impinges upon the defendant’s “substantial rights,” FED. R.
CRIM. P. 52(b), in a way that “seriously affect[s] the fairness,
integrity or public reputation of judicial proceedings,” United
States v. Olano, 507 U.S. 725, 736 (1993) (quoting United
States v. Atkinson, 297 U.S. 157, 160 (1936)). On the record
before us, we cannot find that appellant’s substantial rights
have been affected.

    “A sentencing error affects substantial rights when there is
a reasonable likelihood it impacted the sentence.” Burroughs,
613 F.3d at 245. In light of the District Court’s decision
denying appellant’s motion to dismiss the indictment, it is
implausible to think that the error in this case impacted
appellant’s sentence. The District Court’s decision in Mack
clearly rejected appellant’s “inducement” claim, see Mack, 53
F. Supp. 3d at 188, and that claim is essentially the same as
appellant’s sentencing manipulation argument. The decision
in Mack has not been contested, and for good reason. In our
view, the District Court’s findings, reasoning, and judgment
in Mack are eminently sound.
                              21
C. Drug Weight Calculation

    Finally, appellant argues that the District Court erred in
calculating the drug weight attributable to him. He argues that
the procedure used by MPD and DEA is not a “legally
satisfactory proof of drug quantity.” Br. for Appellant 12. We
review the District Court’s determination of drug quantity
relevant for sentencing under a clear error standard. United
States v. Burnett, 827 F.3d 1108, 1120 (D.C. Cir. 2016).
There was no error here.

    After defense counsel called for an evidentiary hearing to
determine the drug quantity for which appellant would be
accountable, the District Court heard testimony from the
officers who processed the PCP that appellant sold to the
undercover officer. As detailed above, the officers testified
and introduced photographs showing that after they seized
multiple vials containing clear liquid in Mack’s possession,
they field tested each vial for PCP. Then, the officer
calibrated a scale, combined all of the liquid PCP into a
beaker, and weighed the aggregate PCP. Next, the officer
removed a one-ounce sample from the aggregated liquid PCP
in the beaker, packaged it, and sent it to the DEA’s Mid-
Atlantic lab for testing. The officer used this same
methodology to process the vials from both the first and
second drug sales. The District Court credited this testimony
and evidence in upholding MPD procedures. This was not
clear error.

    Defense counsel claims that appellant should only be
accountable for the two one-ounce samples (roughly 50
grams) sent to the DEA’s lab, and not for the aggregate
quantity of PCP in the vials field tested and weighed by MPD.
The District Court rejected this argument after the evidentiary
hearing. Appellant’s sole challenge to this finding is that
                              22
MPD’s testing procedures were not authorized by 28 CFR §
50.21, which appellant claims governs only DEA’s drug
testing procedures. Br. for Appellant 11–12. This argument
misses the mark. MPD’s drug processing procedures do not
need to be authorized by any federal regulations to provide
valid, satisfactory proof of drug quantity. See McCutchen, 992
F.2d at 25–26 (upholding processing technique to determine
drug quantity for sentencing where the government
extrapolated from a test sample).

    “A district court makes findings of drug quantities under
a preponderance of the evidence standard.” Burnett, 827 F.3d
at 1120 (citing United States v. Fields, 325 F.3d 286, 289
(D.C. Cir. 2003)). Appellant has not raised, nor do we
perceive, any error with the District Court’s calculation of
PCP attributable to appellant.

                    III. CONCLUSION

    For the reasons set forth above, we affirm the judgment of
the District Court.
