                 FOR PUBLICATION
 UNITED STATES COURT OF APPEALS
      FOR THE NINTH CIRCUIT

UNITED STATES OF AMERICA,                  No. 06-30242
                Plaintiff-Appellee,
               v.                            D.C. No.
                                          CR-03-00028-DWM
DAVID TORO CHASE,
                                              OPINION
             Defendant-Appellant.
                                      
       Appeal from the United States District Court
               for the District of Montana
       Donald W. Molloy, District Judge, Presiding

                  Argued and Submitted
            June 4, 2007—Seattle, Washington

                   Filed August 27, 2007

     Before: Harry Pregerson, Warren J. Ferguson, and
              Sandra S. Ikuta, Circuit Judges.

                Opinion by Judge Ferguson




                           10569
10572               UNITED STATES v. CHASE


                         COUNSEL

John Rhodes, Assistant Federal Defender, Missoula, Montana,
for the defendant-appellant.

Joshua S. Van de Wetering, Assistant United States Attorney,
Missoula, Montana, for the plaintiff-appellee.


                         OPINION

FERGUSON, Circuit Judge:

   Defendant-Appellant David Toro Chase (“Chase”) appeals
his sentence for conviction of conspiracy to manufacture
methamphetamine. Chase contends that: (1) the district court
erred in denying his request for an expert; (2) the court based
its determination of drug quantity on unreliable evidence; and
(3) the sentence was greater than necessary. We hold that the
district court abused its discretion in denying Chase’s request
for a forensic expert and relied on evidence lacking sufficient
indicia of reliability. We do not reach the third issue.
                        UNITED STATES v. CHASE                       10573
         FACTUAL AND PROCEDURAL BACKGROUND

I.       Initial Proceedings

   Chase pleaded guilty to two counts of conspiracy to manu-
facture methamphetamine, in violation of 21 U.S.C.
§§ 841(a)(1) and 846, and one count of possession of a fire-
arm in a drug trafficking crime, in violation of 18 U.S.C.
§ 924(c)(1)(B)(I). At the first sentencing hearing, Chase con-
tested the quantity of methamphetamine alleged by the gov-
ernment. Chase admitted producing between 109.67 and
164.5 grams in February 2003 at the home of a friend (“the
Mount Avenue location”), but he disputed the combined
quantity allegedly produced between June and October 2003
at two of his previous residences (collectively, “the Twilight
location”).

   The government relied on an expert report for its produc-
tion estimate. The report consisted of a two-page letter
(“letter”) prepared by government expert Scott Edison Rien-
hardt, who, in turn, had relied upon two reports of the State
of Montana Forensic Sciences Division (collectively, “the
State Report”). The State Report listed items and substances
allegedly found at the Twilight location, including chemicals,
equipment, four “recipes” for methamphetamine, and 100
empty boxes of pseudoephedrine, a methamphetamine precur-
sor commonly known by the brand name Sudafed.1 Rienhardt
concluded that, of the four recipes, the “Curbshot” method
was the one most likely to have been utilized, because of the
chemicals listed in the State Report. Two 5,000-milliliter
flasks were listed among the seized equipment. Rienhardt
offered no opinion as to whether either flask had been used,
but he calculated that, following the Curbshot method, a
     1
   Although Rienhardt testified that he had reviewed the State Report in
preparing his expert report, he further testified that he had not been aware
that approximately 100 empty boxes of pseudoephedrine were found at the
lab. The record shows no reason for this discrepancy.
10574                  UNITED STATES v. CHASE
5,000-milliliter flask could be used to produce between 500
and 750 grams of methamphetamine.

   “[B]ased upon the information [ ] contained in the [Rien-
hardt letter],” the district judge estimated that Chase had pro-
duced 500 to 750 grams of methamphetamine at the Twilight
location. He sentenced Chase to eighty-eight months impris-
onment for the drug charges and 120 months for the gun charge.2

  Chase appealed. While his first appeal was pending, the
Supreme Court decided Blakely v. Washington, 542 U.S. 296
(2004). The Ninth Circuit remanded the instant case for recal-
culation and resentencing in light of Blakely.

II.   Second Hearing

   In March 2006, the district judge again heard argument and
considered evidence regarding the quantity of methamphet-
amine Chase had produced. Prior to the presentation of any
testimony, Chase renewed a previously filed, and previously
denied, motion to hire a forensic expert pursuant to 18 U.S.C.
§ 3006A(e)(1). The court denied the motion.

   Rienhardt, the government’s expert, testified at the second
hearing. He explained that he typically estimates drug quanti-
ties based on the “actual chemicals present”—specifically the
known quantities of a drug’s precursors—but in this case the
precursor quantities were unavailable. The State Report did
not indicate the quantities of any chemicals that were identi-
fied, nor the purity levels of any such substances. There was
no information regarding which precursors were on the vari-
ous containers associated with the Twilight location, and there
was “no indication that any of the glassware had methamphet-
amine in it.”
  2
    There is no dispute that the gun charge carries a mandatory minimum
sentence of ten consecutive years and does not affect the calculations in
this case. See 18 U.S.C. § 924(c)(1).
                       UNITED STATES v. CHASE                      10575
   Rienhardt explained that, according to the State Report, the
5,000-milliliter flask—upon which he based his estimate—
had been found in its original box, and there was no evidence
of any chemical trace on the flask. Rienhardt testified that a
number of other glass containers found on the premises could
have been used to produce methamphetamine. Additionally,
he stated that his 500 to 750 gram estimate depended on an
assumption that the 5,000-milliliter flask had been used, but
he expressly disavowed any opinion as to whether this had
actually occurred.

   Defense counsel’s theory of the case was that, based on the
100 empty boxes of pseudoephedrine listed in the State
Report, an accurate estimate of the quantity of methamphet-
amine produced at the Twilight location was forty grams. On
cross-examination, Rienhardt admitted that he had been
unaware of the empty boxes when preparing his letter. Rien-
hardt calculated that if Chase had cooked in small batches,
100 boxes of pseudoephedrine (each containing twenty-four
sixty-milligram pills) would have yielded a combined total of
forty to sixty grams of methamphetamine.

   Chase testified in his own defense. He explained that he
had produced the narcotic for his own use, not for sale, with
red phosphorous obtained from matches and pseudoephedrine
purchased from a drugstore. He testified that he had used a
500-milliliter container, not the 5,000-milliliter flask, and that
each time he had cooked fourteen grams of pseudoephedrine
to produce approximately seven grams of methamphetamine.

   The court concluded that Chase had produced at least 609
grams of methamphetamine, including 100 grams at the
Mount Avenue location and 500 at the Twilight location.
Under the United States Sentencing Guidelines Manual
(“U.S.S.G.” or “Guidelines”), the court rounded downward
and used a 350 to 500 gram estimate to give Chase a base
offense level of thirty. U.S.S.G. § 2D1.1(c)(5).3 With a crimi-
  3
   “If taking the margin of error into account and erring on the side of
caution would reduce the defendant’s base offense level to the next lowest
10576                  UNITED STATES v. CHASE
nal history category II and a three-level decrease for accep-
tance of responsibility, the Guidelines recommended a range
of seventy-eight to ninety-seven months for the drug convic-
tions. U.S.S.G. ch. 5 Pt. A. The court imposed a sentence of
198 months imprisonment, including 120 months for the gun
charge and seventy-eight months for the drug charges. The
court also ordered Chase to pay restitution in the amount of
$16,195.71.

                           DISCUSSION

I.    Did the District Court Err in Denying Chase’s
      Request for a Forensic Expert?

   Under the Criminal Justice Act, 18 U.S.C. § 3006A(e)(1),
“[c]ounsel for a person who is financially unable to obtain . . .
expert . . . services necessary for adequate representation may
request them.” After conducting an inquiry in an ex parte pro-
ceeding, if the court finds “that the services are necessary and
that the person is financially unable to obtain them, the court
. . . shall authorize counsel to obtain the services.” Id. The
decision to grant or deny a request for services under the
Criminal Justice Act will be overturned on appeal where the
district court has committed an abuse of discretion. United
States v. Smith, 893 F.2d 1573, 1580 (9th Cir. 1990).

     A.   Necessity of Services

   [1] Upon a timely request by an indigent defendant, “[t]he
statute requires the district judge to authorize [expert] defense
services . . . in circumstances in which a reasonable attorney
would engage such services for a client having the indepen-
dent financial means to pay for them.” United States v. Bass,
477 F.2d 723, 725 (9th Cir. 1973). The court’s inquiry into

level, the court must do so.” United States v. Scheele, 231 F.3d 492, 499
(9th Cir. 2000) (citations omitted).
                     UNITED STATES v. CHASE                 10577
the necessity of services must be specific to the facts of the
particular case. See, e.g., United States v. Armstrong, 621
F.2d 951, 956 (9th Cir. 1980).

   [2] In a drug case, the sentence depends primarily on the
quantity of narcotics that the court attributes to the defendant.
U.S.S.G. §§ 2D1.1, 3D1.2(d), ch. 5 Pt. A. Therefore, from the
perspective of defense counsel, formulating a theory of drug
quantity is critical. In this case in particular, the only disputed
issue was the quantity of methamphetamine produced at the
Twilight location, where no methamphetamine was found, so
the determination of drug quantity demanded a scientific cal-
culation. Chase reasonably requested the appointment of an
expert in forensic chemistry to assist his attorney in formulat-
ing a theory of the quantity of methamphetamine and to rebut
that of the government’s expert.

   On appeal, the government asserts that defense counsel’s
cross examination of Rienhardt proved to be sufficient and
therefore Chase had no need to hire his own expert. Essen-
tially, the government argues, because Rienhardt agreed with
defense counsel’s calculation—100 boxes of pseudoephedrine
yields forty to sixty grams of methamphetamine—“[t]here
was nothing for an outside expert to prove.” This argument
misses the point.

   While there appears to be no dispute that 100 boxes of
pseudoephedrine can produce approximately forty to sixty
grams of methamphetamine, the value of the empty boxes as
an indicator of the lab’s production capacity is hotly con-
tested. The government’s expert offered no opinion as to the
best available method for estimating drug quantity. The
appropriateness of relying on the glass flask, the empty boxes,
or some other method is by no means settled, and a defense
expert could have informed that discussion.

   [3] Although the burden of proof of drug quantity lies with
the prosecutor, Chase had a right to put on a defense, and to
10578               UNITED STATES v. CHASE
retain an expert if “a reasonable attorney would [have] eng-
age[d] such services for a client having the independent finan-
cial means to pay for them.” Bass, 477 F.2d at 725. “[T]he
Fourteenth Amendment’s due process guarantee of fundamen-
tal fairness” requires that the “basic tools of an adequate
defense . . . be provided to those defendants who cannot
afford to pay for them.” Ake v. Oklahoma, 470 U.S. 68, 76,
77 (1985) (quotations omitted). The Supreme Court has “long
recognized . . . that . . . justice cannot be equal where, simply
as a result of his poverty, a defendant is denied the opportu-
nity to participate meaningfully in a judicial proceeding in
which his liberty is at stake.” Id. at 76. In this case, Chase had
a right to hire an expert who could have produced his or her
own “investigation, interpretation, and testimony.” Id. at 80.

   [4] Additionally, the aid of an expert could have made the
cross-examination of Rienhardt more effective. Informed by
an expert, Chase’s attorney could have asked Rienhardt more
specific questions about the formula he used, flaws in that for-
mula, and any additional factors that he should have consid-
ered. The attorney could have posed more sophisticated
inquiries concerning the literature and experience upon which
Rienhardt based his opinion, whether he was familiar with
other literature in the field, and whether he would have con-
ceded that other estimation methods might be preferable to
the one he had used in this case.

   The absence of a cross-examination informed by scientific
knowledge was highlighted when the district judge asked
Rienhardt to play the role of a defense expert. The court asked
the government’s expert to attack the validity of his own posi-
tion:

    THE COURT: All right. Now, if you were asked to
    attack the method you used, how would you do it?

    THE WITNESS: If I was going to try to refute what
    I said?
                       UNITED STATES v. CHASE                       10579
      THE COURT: Challenge what you said?

      THE WITNESS: . . . I don’t — I couldn’t attack
      myself. . . .

Clearly, both the defendant and the court would have benefit-
ted from the services of a defense expert.4

   [5] At least one other circuit recently recognized the neces-
sity of a defense expert in a sentencing hearing involving
methamphetamine estimation. See United States v. Hardin,
437 F.3d 463, 470 (5th Cir. 2006). In Hardin, the defendant-
appellant asserted that “bones” were a methamphetamine
byproduct, which should not have been included in a narcotics
calculation. Id. at 466. The Court of Appeals ruled that the
district court had erred in denying funds for a defense expert
to testify “on [this] disputed factual issue regarding [quantity,]
the primary issue [in the defendant’s] sentence determina-
tion.” Id. at 470. The Fifth Circuit held that the district judge’s
denial of the motion for appointment of a chemical expert
“when necessary to respond to the government’s case against
[the defendant], where the government’s case rest[ed] heavily
on a theory most competently addressed by expert testimony,”
constituted an abuse of discretion. Id. at 468 (citations and
quotation omitted). The Court of Appeals ordered the district
judge to appoint the requested expert and to re-sentence the
defendant after taking expert testimony. Id. at 471.5
  4
     The government cites United States v. Labansat, 94 F.3d 527, 530 (9th
Cir. 1990), in which we decided that a cross-examination was sufficient
without a defense expert on eyewitness identification. Labansat is inappo-
site. Nothing about the prosecutor’s theory in that case raised scientific
issues; the witnesses were laypersons recounting personal observations of
a bank robbery. Id. at 529. Moreover, while psychological expertise might
inform some cases involving eyewitness testimony, see, e.g., Michael R.
Leippe, The Case for Expert Testimony About Eyewitness Memory, 1 Psy-
chol. Pub. Pol’y & L. 909 (1995), in Labansat, the defendant’s sister iden-
tified her brother on the bank’s surveillance video. 94 F.3d at 529.
   5
     Hardin also required the lower court to take testimony from any rele-
vant expert tendered by the government; apparently, no such expert had
10580                  UNITED STATES v. CHASE
   [6] In the case before us, the district court denied Chase’s
motion to hire an expert on the basis that its estimation of
drug quantity did not depend on a finding that Chase used the
5,000-milliliter flask. However, the court did not clarify how
it reached its estimate if not for the assumption about the
flask, and, indeed, the record specifically reflected that the
court estimated a production of 500 to 750 grams of metham-
phetamine “[b]ased upon the information [ ] contained in the
Rienhardt [letter].” Given this record, the district court’s
explanation for denying the motion to hire an expert was
unreasonable.

  B.    Prejudice

   An appellate court will overturn a district court’s denial of
a request for an expert only where the defendant has demon-
strated prejudice. United States v. Sims, 617 F.2d 1371, 1375
(9th Cir. 1980). The prejudice cannot be merely speculative;
it must be demonstrated by clear and convincing evidence. Id.
The harm in this case is clearly demonstrated.

   The district court explicitly relied on the government’s
expert testimony to estimate a drug quantity of 600 grams,
including 500 grams from the Twilight location. Based on that
quantity and a downward adjustment of one level to account
for any margin of error, the court assigned Chase a base
offense level of thirty. With a three-level adjustment for
Chase’s acceptance of responsibility, this resulted in a level
of twenty-seven, and, under criminal history category II,
Chase received a Guidelines range of seventy-eight to ninety-
seven months for the drug charges. U.S.S.G. ch. 5 Pt. A. The
court adopted the Guidelines recommendation and sentenced
Chase to seventy-eight months of imprisonment (not includ-
ing the sentence for the gun charge).

testified previously. Id. Chase’s situation seems even more unfair than
Hardin’s, because the government in the instant matter benefitted from an
expert who provided both live testimony and a written statement.
                    UNITED STATES v. CHASE                10581
    [7] Chase argued at his sentencing hearing that a more
plausible estimate of his production at the Twilight location
was forty grams of methamphetamine. Had Chase been per-
mitted to retain an expert who provided testimony substantiat-
ing this estimate, and had the district court credited that
testimony, Chase’s responsibility would have fallen within the
range of fifty to 200 grams (forty grams from the Twilight
location plus 109 from the Mount Avenue location), produc-
ing a base offense level of twenty-six. U.S.S.G. § 2D1.1(c)(7).
Given Chase’s acceptance of responsibility, Chase would
have had an offense level of twenty-three. In contrast to the
seventy-eight months of imprisonment assigned, the sentenc-
ing range for an offense level of twenty-three is fifty-one to
sixty-three months. U.S.S.G. ch. 5 Pt. A. Even if the judge
had sentenced Chase to the maximum time within the Guide-
lines for level twenty-three, the sentence would have been
sixty-three months. The assigned prison term exceeds this
amount by over a year. “[A]ny amount of actual jail time has
. . . significance.” Glover v. United States, 531 U.S. 198, 203
(2001). Therefore, Chase has demonstrated prejudice.

   [8] For the foregoing reasons, the district court abused its
discretion in denying Chase an opportunity to retain an expert,
and Chase was prejudiced by this error.

II.   Was the District Court’s Approximation of Drug
      Quantity Erroneous?

    Under the Sentencing Guidelines, “[w]here there is no drug
seizure or the amount seized does not reflect the scale of the
offense,” a district court may estimate the quantity of the drug
and may consider “the size or capability of any laboratory
involved.” U.S.S.G. § 2D.1.1 cmt. n.12; see, e.g., United
States v. Putney, 906 F.2d 477, 479 (9th Cir. 1990). “Whether
the method adopted by the district court to approximate the
relevant quantity of drugs is proper under the Guidelines is
. . . reviewed de novo,” United States v. Culps, 300 F.3d 1069,
1076 (9th Cir. 2002), and factual findings related to the capa-
10582               UNITED STATES v. CHASE
bility of a drug operation are reviewed for clear error. United
States v. Rosacker, 314 F.3d 422, 427 (9th Cir. 2002).

   “ ‘Approximations of drug quantity must meet three
criteria.’ ” United States v. Kilby, 443 F.3d 1135, 1141 (9th
Cir. 2006) (quoting Culps, 300 F.3d at 1076). “First, . . . the
government is required to prove the approximate quantity by
a preponderance of the evidence . . . . Second, the information
which supports an approximation must possess sufficient indi-
cia of reliability to support its probable accuracy. Third, . . .
the district court must err on the side of caution in calculating
approximated drug quantity.” Culps, 300 F.3d at 1076 (inter-
nal quotations, citations, and punctuation omitted).

  A.    Insufficient Indicia of Reliability for Court’s
        Estimate

   [9] The district court’s approximation of drug quantity
lacked “sufficient indicia of reliability.” Culps, 300 F.3d at
1076. The judge explicitly stated that his estimate was based
on the Rienhardt letter and testimony, which opined that a
5,000-milliliter flask could yield 500 to 750 milligrams of
methamphetamine. This calculation was unreliable.

   Rienhardt’s letter readily admitted that the State Report was
insufficient for him to estimate the quantity of methamphet-
amine Chase had produced:

    There were no weights/volumes or purity results
    reported for the exhibits that contained ephedrine/
    pseudoephedrine, a required precursor in the synthe-
    sis of methamphetamine. A production estimate can-
    not be determined without weight/volume and purity
    results for the exhibits. There was also not a correla-
    tion between the exhibits seized at the [Twilight
    location] and the [State Report].

  Given the limitations of the data provided to him, Rienhardt
calculated a theoretical yield for the 5,000-milliliter flask.
                    UNITED STATES v. CHASE                10583
However, he emphasized that the 500 to 750 gram estimate in
his letter was “just a capability based on glassware.” The esti-
mate depended on an assumption that the 5,000-milliliter
flask had been used, but he testified that “any number of”
other glass jars in which methamphetamine could have been
produced were reported to have been found on the premises.
When the court asked Rienhardt why he assumed that the
5,000-milliliter flask—or any other glassware—had been
used, Rienhardt responded that he had made no such assump-
tion.

   [10] We have made clear that “the relevant inquiry [is] not
what a theoretical maximum yield would be, or even what an
average methamphetamine cook would produce, but what
[the] appellant[ ] [himself] could produce.” Rosacker, 314
F.3d at 428 (quotation omitted). The government’s expert
quite candidly admitted that his calculation was a maximum
theoretical yield. He explained, “I was just saying the most,
based on what was there, that’s the most that could be pro-
duced using that glassware.” This approach was unreliable as
a method of estimating how much methamphetamine Chase
produced.

   The government asserts that this court has previously
approved the use of glassware to assess lab capability. The
government relies on United States v. Williams, 989 F.2d
1061 (9th Cir. 1993), but the methamphetamine estimate in
that case reflected the amount of narcotics the defendant
could have produced in the assorted glassware at the lab given
the quantity of precursor chemicals seized from the property.
Id. at 1073 & n.5. In this case, no measured quantity of pre-
cursor was seized.

  We also upheld an estimate based in part on glassware in
United States v. August, 86 F.3d 151, 152-53 (9th Cir. 1996),
but that case is quite distinct because of the overwhelming
evidence that the district court had considered in connection
with the glassware. In August, police officers had seized
10584               UNITED STATES v. CHASE
twenty kilograms of waste material from the site. Id. at 152.
Additionally, extensive testimony from lay witnesses and a
forensic chemist demonstrated that the defendants had pur-
chased enough hydriodic acid to produce between 2,000 and
3,000 grams of methamphetamine, that the defendants had
been observed in possession of approximately 1.36 kilograms
of methamphetamine, and that the lab was visited by a
“steady stream of customers.” Id. at 152-53. Because the
waste material provided abundant evidence of more than one
reaction, we held that it was reasonable for the district court
to have taken “the minimum estimate [that the flask could
have produced] and multiplied it by two to reflect the fact that
at least two reactions [had] occurred.” Id. at 155 (emphasis
altered).

   [11] Rienhardt’s glassware estimate, in contrast, had no
reliable evidentiary basis. As Rienhardt testified, to his
knowledge, no methamphetamine was seized and no mea-
sured quantities of precursors were found at the Twilight loca-
tion. Unlike in August, where the twenty kilograms of waste
material indicated a large-scale drug operation, no physical
evidence in Chase’s case corroborated Rienhardt’s estimation.
To the extent the district court’s approximation of drug quan-
tity relied on Rienhardt’s glassware estimate, the district court
erred.

  B.    Insufficient Indicia of Reliability for Alternative
        Ruling

   The district court provided an alternative basis for its sen-
tencing decision. Even if the court had accepted Chase’s the-
ory that the 100 empty boxes of pseudoephedrine
demonstrated the production of forty grams of methamphet-
amine, the district court explained that it would have multi-
plied those forty grams by eight to account for the number of
months that he believed Chase had occupied the Twilight
location. This calculation would have led to the same sentenc-
ing range that resulted from the Rienhardt method.
                    UNITED STATES v. CHASE                 10585
   This analysis was unreasonable. The court assumed that
Chase cooked once per month, that he cooked 100 boxes of
pseudoephedrine on each occasion, and that he did so for
eight months. The record contains “no reliable evidentiary
basis for any of the pivotal assumptions in the drug quantity
approximation.” Rosacker, 314 F.3d at 429. The only evi-
dence at all relevant to these assumptions was Chase’s own
testimony that he cooked the contents of the 100 boxes in
small batches over a period of time.

   Under the accepted “multiplier” method of estimating drug
quantity, a court first estimates a daily or weekly quantity,
then estimates the period of time over which the activity
occurred, and then calculates the total. Culps, 300 F.3d at
1077. But this is permissible only where there are sufficient
indicia of reliability for each of the figures included in the
equation. Id. “[T]his method necessarily fails when any single
variable cannot be ascertained by a preponderance of the evi-
dence.” Id. at 1082.

   “We insist . . . that in establishing the facts, including
approximations[ ] underlying a sentence, the district court uti-
lize only evidence that possesses sufficient indicia of reliabil-
ity to support its probable accuracy.” United States v. Garcia-
Sanchez, 189 F.3d 1143, 1148 (9th Cir. 1999) (quotation and
internal punctuation omitted); see also id. at 1149 (“[A]
defendant [has a] due process right to ensure the reliability of
information used at sentencing.”). If given the choice between
a “more reliable method” that “may produce a significant
underestimate” and a different method that lacks a proper evi-
dentiary basis, the court must choose the reliable method,
even if a significant underestimate results. Kilby, 443 F.3d at
1142 n. 4. Where, as here, the record contains no evidence
that permits the use of the multiplier method, it simply cannot
be used. Culps, 300 F.3d at 1077.

  [12] The court relied on evidence lacking sufficient indicia
10586                   UNITED STATES v. CHASE
of reliability. The approximation of drug quantity and result-
ing sentence were therefore erroneous.6

III.    Was the Sentence Unreasonable Because It Was
        Greater than Necessary?

   We do not reach Chase’s final assertion that his sentence
was unreasonable because it was greater than necessary. “If
there was a material error in the Guidelines calculation, [the
court] will remand for resentencing, without reaching the
question of whether the sentence as a whole is reasonable.”
Kilby, 443 F.3d at 1140 (citation omitted).

                            CONCLUSION

   [13] We conclude that the denial of an expert constituted an
abuse of discretion, and that the district court relied on unreli-
able evidence. We therefore reverse the denial of the expert,
vacate the sentence below, and remand. If, after taking expert
testimony, the district court concludes that the government
and the appellant have presented equally plausible methods of
estimating drug quantity, the court shall be careful to err on
the side of caution and choose the more conservative of the
two. See August, 86 F.3d at 154; United States v. Alvarez, 358
F.3d 1194, 1212-13 (9th Cir. 2004); Scheele, 231 F.3d at 498.
The court shall re-sentence the appellant in accordance with
  6
   We recognize that Rienhardt assumed a fifty to seventy-five percent
production rate, not a full 100%, and we appreciate that the district court
rounded down the total estimate of methamphetamine. However, these
efforts had no bearing on the reliability of Rienhardt’s formula. See, e.g.,
Rosacker, 314 F.3d at 426 (“[C]haracterization of [an] estimate as ‘conser-
vative’ does not substitute [for] the lack of a ‘reliable evidentiary basis’
for the estimate.” ) (quotation omitted). In spite of the court’s attempt to
“err[ ] most generously” in Chase’s favor, its calculation resulted in a base
offense level two levels higher than that which Chase alleged the more
conservative method would have produced.
                    UNITED STATES v. CHASE   10587
the rulings set forth herein.

  REVERSED, VACATED and REMANDED.
