Opinion by Judge BRIGHT; Dissent by Judge REINHARDT
BRIGHT, Circuit Judge:A jury convicted Benjamin Corona-Garcia of reentering the United States after he had been previously deported, a violation of 8 U.S.C. § 1326(a). Corona-Garcia appeals and challenges both his conviction and sentence. Although we uphold Corona-Garcia’s conviction because he was entitled to neither substitution of counsel nor judgment of acquittal, as he argues, we nevertheless agree with Corona-Garcia’s contention that he was entitled to a three-level sentencing reduction for acceptance of responsibility rather than the two-level reduction he received. As a result, we VACATE his sentence and REMAND.
I. BACKGROUND
Benjamin Corona-Garcia (“Corona-Garcia”) is a native and citizen of Mexico. While incarcerated in California for state crimes, the INS interviewed Corona-Garcia as part of an “Institutional Hearing Program” in which suspected criminal aliens are subjected to questioning. In his interview with an INS officer, and without the benefit of Miranda, Corona-Garcia admitted that: (1) he is a Mexican citizen; (2) he had previously been deported to Mexico from the United States; (3) he reentered the United States near Calexico, California, by “jumping the fence” sometime in April 1997; and (4) he had neither sought nor received permission to reenter the United States. See Trial Tr. at 59.
When Corona-Garcia was eventually paroled by the state, he was transferred to the custody of the INS. On March 23, *9751998, while housed in an INS detention center in San Diego, Corona-Garcia was interviewed by a second INS investigator, Special Agent Welch. Agent Welch informed Corona-Garcia of his rights: She read him the standard Miranda warnings from a pre-printed card, both in English and in Spanish, and insured his understanding by asking for explicit affirmative .responses after each line of written .text. Corona-Garcia acknowledged that he understood his rights, and then he again confessed that he is a citizen of Mexico, that he had been deported, and that after this deportation he entered the United States near Calexico without inspection or permission. See id. at 109-10. Based on this confession, Agent Welch referred the case to the United States Attorney for prosecution.
On March 31, 1998, a grand jury indicted Corona-Garcia and alleged that:
On or about April 1997, within the Southern District of California, defendant BENJAMIN CORONA-GARCIA, an alien, after having been deported and removed from the United States to Mexico, through the Port of Entry, Calexico, California, on or about December 16, 1996, entered in San Diego County, without the Attorney General of the United States having expressly consented to the defendant’s reapplication for admission into the United States; in violation of Title 8, United States Code, Section 1326.
E.R. at 1-2 (emphasis added).
Subsection (a) of 8 U.S.C. § 1326, titled “Reentry of removed aliens,” states in relevant part that:
Subject to subsection (b) of this section, any alien who—
(1) has been denied admission, excluded, deported, or removed or has departed the United States while an order of exclusion, deportation, or removal is outstanding, and thereafter
(2) enters, attempts to enter, or is at any time found in, the United States, unless ... the Attorney General has expressly consented to such alien’s reapplying for admission ... [shall be subject to criminal penalties].
8 U.S.C. § 1326'(1999) (emphasis added).
On the morning of trial, with a pool of prospective jurors waiting to be impaneled, Corona-Garcia moved for substitution of counsel. The district court promptly held a sealed, ex parte proceeding (subsequently unsealed) at which Corona-Garcia’s counsel informed the court that, although he was prepared for trial, he and his client disagreed' on undisclosed matters of trial strategy. Addressing the court, Corona-Garcia indicated that he was confused, upset, and failing to communicate with his lawyer. After extensive efforts to elicit further information from both Corona-Garcia and his lawyer, the district court found that the basis offered for substituting counsel was inadequate and presented a substantial likelihood of inconvenience and delay. On that basis, the court denied the motion.
After opening arguments, Corona-Garcia moved to. suppress his confessions. The district court heard extended argument on the question and agreed that the INS took Corona-Garcia’s first admission in violation of his Fifth Amendment rights. The court suppressed the confession on that basis. However, with respect to his second admission, the court found that Corona-Garcia’s confession to Agent Welch was made under conditions which complied with Miranda. As a result, the court ruled that Corona-Garcia’s confession to Agent Welch could be presented to the jury.
During trial, the government introduced several documents from Corona-Garcia’s INS file. These documents showed that Corona-Garcia had been found deportable by an immigration judge in November 1996, see Ex. 3, and that he had in fact been deported at the Calexico border station in December 1996 pursuant to a Warrant of Deportation. See Ex. 4. The government also introduced a so-called “Certificate of Non-Existence.” See Ex. 6. This certificate showed that the INS *976conducted a search of both its automated and non-automated records and, after so doing, found no records pertaining to any applications for permission to reenter the United States by Corona-Garcia subsequent to his 1996 deportation.
Testimony was also given by several witnesses. Torres, a fingerprint expert from the San Diego Police Department, testified that the fingerprint card attached to Corona-Gareia’s 1996 Warrant of Deportation matched a fingerprint exemplar taken from Corona-Garcia a few days before trial. McCormack, an immigration enforcement officer, testified that he witnessed Corona-Garcia’s physical deportation at the Calexico border station on December 16, 1996. Carvajal, an INS agent, testified about the nature and contents of several of the INS documents introduced as exhibits, including the Certificate of Non-Existence. Finally, and most importantly, Agent Welch testified to the form and content of her interview with Corona-Garcia.
At the close of the government’s evidence, and arguing that it had failed to show that he entered the United States illegally, Corona-Garcia moved for judgment of acquittal under Rule 29. After extended argument on this contention, the district court concluded that adequate evidence had been presented by the government for a jury to find all of the elements of a § 1326 violation beyond a reasonable doubt,1 and specifically that Corona-Garcia had entered the United States. On that basis, the court denied the motion.
Corona-Garcia presented no witnesses and offered no evidence beyond several INS documents introduced as defense exhibits during cross-examination. After brief deliberations, the jury returned a verdict of guilty. On August 25, 1998, the district court sentenced Corona-Garcia to eighty-four months in prison. This sentence was at the bottom of the guideline range for an offender with a criminal history score of 23 and an offense level of 22. The district court reached this offense level calculation, in part, because it granted Corona-Garcia a two level reduction under United States Sentencing Guidelines (“U.S.S.G.”) § 3El.l(a) for acceptance of responsibility. However, the court refused to grant an additional one-level reduction under U.S.S.G. § 3El.l(b)(l). Although Corona-Garcia argued that he was entitled to this further reduction because he confessed fully even before the onset of his prosecution, the district court reasoned that an additional one-point reduction under § 3El.l(b)(l) was not proper because “[t]here was no timely notice of a plea of guilty nor was there a plea of guilty.” Sent. Tr. at 192.
On August 31, 1998, Corona-Garcia timely appealed to this court. He now asserts three errors.
II. DISCUSSION
A. Substitution of Counsel.
Corona-Garcia argues that the district court erroneously denied his motion for substitution of counsel. We review the denial of such motions for abuse of discretion. See United States v. Castro, 972 F.2d 1107, 1109 (9th Cir.1992).
We focus on three considerations when addressing whether a defendant was wrongly denied the opportunity to substitute counsel: first, we consider whether the district court’s inquiry on the matter was adequate; second, we study the extent of the conflict between the defendant and his counsel; and third, we weigh the timeliness of the motion against any inconvenience or delay that would result from granting the motion. See United States v. D’Amore, 56 F.3d 1202, 1204-05 (9th Cir.1995), overruled on other grounds by United States v. Garrett, 179 F.3d 1143, 1145 *977(9th Cir.1999) (en banc). In this case, it is clear that these considerations incline sharply toward refusing Corona-Garcia's motion for substitution of counsel.
First, when Corona-Garcia moved for substitution of counsel, the court immediately suspended the proceedings, cleared the courtroom, and held an ex parte hearing on the motion. At this hearing, the court inquired about the reasons and support for the motion and examined both Corona-Garcia and his trial counsel at length. Corona-Garcia explained to the court that he was having family problems, that he felt "lost and confused," Hearing Tr. at 2, and that he and his lawyer were "not communicating with each other." Id. at 3. For his part, Corona-Garcia's counsel explained that he was "prepared to go forward," id. at 4, and that he had been communicating with his client, but he also indicated that Corona-Garcia disagreed with him about some fundamental issues of trial strategy. See id. at 8. Although the court attempted repeatedly to elicit further elaboration from both Corona-Garcia and his counsel, neither person would provide any detail. Under these circumstances, we believe that the district court conducted an inquiry which was as extensive as can reasonably be expected and one which was fully adequate.
Second, the extent of the conflict between Corona-Garcia and his lawyer does not appear to have been severe. Although Corona-Garcia claimed that he was not receiving appropriate "paperwork," Hearing Tr. at 4, neither he nor his lawyer could specify a single document which Corona-Garcia had not received. Id. at 8-9. The only genuine conflict appears to have been with respect to trial strategy. Despite the court's repeated attempts to expose this conflict to scrutiny, both Corona-Garcia and his lawyer refused to provide any meaningful detail. See id. at 5, 6, 8, and 9. On other matters, despite vague assertions to the contrary, both Corona-Garcia and his lawyer admitted that they were in fact communicating. See id. at 3, 5. Thus, our examination of the record reveals that although there was some limited conflict between Corona-Garcia and his lawyer, it was not extensive.2
Third, the motion-brought as it was with trial imminent-would cause inconvenience and delay, both to the court and the prosecution. A defendant's late notice may not be enough alone to prevent substitution of counsel. See United States v. Torres-Rodriguez, 930 F.2d 1375, 1380-81 (9th Ctr.1991) (reversing conviction despite request for substitution made on day of trial) overruled on other grounds by Bailey v. United States, 516 U.S. 137, 116 S.Ct. 501, 133 L.Ed.2d 472 (1995). But when late notice and motion are combined, as they are here, with unpersuasive, chimerical arguments, the case for delay is weak. In addition, Corona-Garcia requested that his trial be conducted expeditiously and both the court and government cleared their calendars to accommodate him, see Tr. of Motion Hearing, May 18, 1998, yet upon making his motion Corona-Garcia had no other counsel waiting to substitute. Under these conditions, and with veniremen waiting for voir dire, we conclude (as did the district court) that the inconvenience caused by any delay would have been substantial and the cost to the court in terms of judicial resources would have been high.
Thus, under the totality of these circumstances, we cannot say that the district court abused its broad discretion when it denied Corona-Garcia's request for substitution of counsel.
B. Judgment of Acquitt at.
At the close of the government's case, Corona-Garcia moved for judgment of acquittal under Rule 29. In support of his motion, Corona-Garcia argued that despite *978his confession the government had not proven all of the elements necessary far the jury to find a violation of § 1326(a), and, in conformity with the common law rule of corpus delicti, as modified by Opper v. United States, 348 U.S. 84, 89-93, 75 S.Ct. 158, 99 L.Ed. 101 (1954) and United States v. Lopez-Alvarez, 970 F.2d 583, 590-93 (9th Cir.1992), that he was therefore entitled to acquittal as a matter of law. Specifically, Corona-Garcia argued that the government had not adduced sufficient tangible, independent evidence to corroborate his admission that he had entered the United States. After a hearing on the matter, the district court denied the motion. Although the court did not articulate its reasons in detail, the court suggested that any necessary corroboration of Corona-Garcia's entry was provided by his mere presence in the courtroom.
Corona-Garcia renews this argument on appeal and contends that the district court erred when it denied his motion for acquittal. We review such contentions de novo and ask whether, "after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." United States v. Bahena-Cardenas, 70 F.3d 1071, 1072-73 (9th Cir.1995) (citations and emphasis omitted).
The only element of the crime in contest here is whether the government presented adequate evidence concerning Corona-Garcia's entry into the United States. The primary evidence against Corona-Garcia in this regard consists of his own confession: He admitted that he entered the United States along the Mexican border near Calexico, in San Diego County, California, sometime in April 1997.
Although the government may rely on a defendant's confession to meet its burden of proof, it has nevertheless been long established that, in order to serve as the basis for conviction, the government must also adduce some independent corroborating evidence. See Opper, 348 U.S. at 89, 75 S.Ct. 158. Under Opper, such corroborating evidence must "tend to establish the trustworthiness of" defendant's admission. Id. at 93, 75 S.Ct. 158. Although independent evidence is not necessary to establish the whole of the corpus delicti, see id., such evidence must "sup-portE ] the essential facts admitted sufficiently to justify a jury inference of their truth." Id. In this regard, we have noted that Opper "rejected the traditional corpus delicti rule and held that the prosecution need not introduce independent evidence of every element of the crime." Lopez-Alvarez, 970 F.2d at 591. Opper also "adopted the new requirement that the prosecution introduce evidence `tend[ing] to establish the trustworthiness of the statement.'" Id. (quoting Opper, 348 U.S. at 93, 75 S.Ct. 158).
Lopez-Alvarez summarized Opper's two-part corroboration requirement this way:
[F]irst, although the state need not introduce independent evidence of the corpus delicti in conformance with the traditional test, it must introduce sufficient evidence to establish that the criminal conduct at the core of the offense has occurred. Second, it must introduce independent evidence tending to establish the trustworthiness of the admissions, unless the confession is, by virtue of special circumstances, inherently reliable ... only then will the evidence be deemed sufficient in a case in which the conviction depends in part on such admission.
Lopez-Alvarez, 970 F.2d at 592.
The gravamen of the offense in this case-that is to say the conduct at the core of the offense-is entry.3 Although *979Corona-Garda maintains that only Ms bald confession supports a conclusion that he entered the United States, we disagree. Under the constellation of corroborating evidence presented by the government, and viewing that evidence in the light most favorable to the prosecution, as we are obliged to do, we believe that a rational trier of fact could have found beyond a reasonable doubt that Corona-Gareia entered the United States.
Corona-Garcia’s presence in the United States is important in this regard. Because the government established that it deported Corona-Gareia to Mexico in December of 1996, it is true by force of common sense that his subsequent presence in the United States demonstrates some form of entry and, a fortiori, corroborates his admission to entry. Thus, because entry is the “conduct at the core of the offense,” Lopez-Alvarez, 970 F.2d at 592, Corona-Garcia’s mere presence in the UMted States helps satisfy the first part of the Opper/Lopez-Alvarez test.
The second part of the test requires evidence tending to establish that the defendant’s confession was trustworthy. In this regard, we believe that an inference may be fairly drawn from Corona-Garcia’s prior deportation at Calexico and his admission that he subsequently reentered the United States near there. This inference, and the detail upon which it relies, is not insignificant because it provides a logical connection between Corona-Gareia and an otherwise random entry point along the long Mexican frontier. Hence, Corona-Garcia’s prior deportation at Calexico lends support to his confession and tends to establish that it was trustworthy.
Although it is true that the sum total of this evidence might well be insufficient, standing alone, to prove entry, we do not read Opper or Lopez-Alvarez to require such absolute proof. Indeed, Opper and Lopez-Alvarez require corroboration of the defendant’s confession — that is to say evidence that fortifies, augments, or supports it4 — from which a jury may infer that the defendant’s confession was a trustworthy admission to core conduct that actually occurred. Corona-Garcia’s presence in the United States may not prove he entered the United States near Calexi-co in April 1997, but it certainly goes far to confirm his admission that he did. Corona-Garcia’s deportation at Calexico does not prove that he reentered near there, but that coincidental fact does strengthen the credibility of his confession.
Therefore, notwithstanding Corona-Garcia’s protestations to the contrary, the district court did not err when it denied his motion for judgment of acquittal.
*980C. Downward Departure for Acceptance of Responsibility.
Finally, Corona-Garcia also challenges his sentence. At his sentencing hearing, the district court granted a two-level reduction for acceptance of responsibility, pursuant to § 3E1.1(a) of the Sentencing Guidelines. The court refused, however, to grant an additional one level reduction under § 3E1.1(b)(1). "`Whether a defendant is entitled to an adjustment based on acceptance of responsibility is a factual determination reviewed for clear error.'" United States v. Blanco-Gallegos, 188 F.3d 1072, 1076 (9th Cir.1999) (quoting United States v. Villasenor-Cesar, 114 F.3d 970, 973 (9th Cir.1997)).
Corona-Garcia argues that, because the district court found that a two-level reduction was warranted, he was then entitled to an additional one-level reduction by virtue of his full and prompt confession to INS investigators. We agree.
Section 31111.1, titled "Acceptance of Responsibility," requires that:
(a) [i]f the defendant clearly demonstrates acceptance of responsibility for his offense, decrease offense level by 2 levels.
(b) [i]f the defendant qualifies for a decrease under subsection (a), the offense level determined prior to the operation of subsection (a) is level 16 or greater, and the defendant has assisted authorities in the investigation or prosecution of his own misconduct by taking one or more of the following steps:
(1) timely providing complete information to the government concerning his own involvement in the offense; or
(2) timely notifying authorities of his intention to enter a plea of guilty, thereby permitting the government to avoid preparing for trial and permitting the court to allocate its resources efficiently,
decrease the offense level by 1 additional level.
U.S.S.G. § 3E1.1.
Presuming that a defendant has quail-fled for the initial two-level reduction under subsection (a), the disjunctive language of subsection (b)-using as it does the word "or"-clearly indicates that a defendant is eligible for an additional one-level reduction if he "timely provid[es] complete information" about his involvement in the crime, irrespective of his plea. Indeed, we have previously held that once it has been established that a defendant has fulfilled the conditions for an acceptance of responsibility reduction under § 3E1.1(a), an additional one-level reduction is mandatory if the defendant meets the independent criteria of either subsection (b)(1) or subsection (b)(2). See United States v. Eyler, 67 F.3d 1386, 1391 (9th Cir.1995). If a defendant makes a timely and complete confession, he satisfies the requirements of § 3E1.1(b)(1) and his subsequent decision to plead not guilty-or even to seek suppression of his confession-is irrelevant.
Here, although Corona-Garcia did put the government to its burden of proof and demanded a speedy trial, he also provided the government with timely and complete information concerning his reentry following deportation. Corona-Garcia made detailed confessions to two INS investigators before he was charged. In fact, he did so before he was even referred for prosecution. This confession established all of the necessary elements of a § 1326 violation: Corona-Garcia admitted that he is an alien, confirmed that he had been previously deported, acknowledged that he reentered the United States, and conceded that he did so without the permission of the Attorney General. No more is required. See Blanco-Gallegos, 188 F.3d at 1077 (timely and complete confession to all elements of § 1326 violation entitles defendant to § 3E1.1(b)(1) reduction).
Thus, in addition to the two-level reduction already granted by the district court under U.S.S.G. § 3E1.1(a), Corona-Garcia *981was entitled to a one-level reduction for acceptance of responsibility under § 3El.l(b)(l). The district court’s conclusion to the contrary was clear error.
III. CONCLUSION
Corona-Garcia’s conviction under 8 U.S.C. § 1326(a) is AFFIRMED. The case is, however, REMANDED for resen-tencing. The district court is directed to grant a three-level reduction for acceptance of responsibility in conformity with this opinion.
. In this case, reading the statute and the indictment together, in order to prove a violation of § 1326 the government needed to prove the following elements as a matter of law: (1) that Corona-Garcia is an alien; (2) that he had been previously deported; (3) that he entered the United States in San Diego County; and (4) that he had not received permission from the INS to reenter before so doing. See 8 U.S.C. § 1326(a); E.R. at 1-2.
. Even if we were to conclude that the conflict with respect to trial tactics was severe, however, we would still be disinclined to reverse on that ground because trial tactics are clearly within the realm of powers committed to the discretion of defense counsel in any event. See United States v. Wadsworth, 830 F.2d 1500, 1509 (9th Cir.1987).
. In reaching this conclusion, we expressly reject Corona-Garcia's contention that "illegal entry" is the gravamen of the offense. We do so for reasons that are clear from the text of § 1326 itself. That section refers to an alien who "enters, attempts to enter, or is at any time found in, the United States." 8 U.S.C. § 1326(a)(2). Notably absent from the statute is any inclusion of, or reference to, "illegal entry." Indeed, under § 1326, entry *979becomes "illegal” only if the Attorney General has not "expressly consented to such alien's reapplying for admission.” 8 U.S.C. § 1326(a)(2)(A). Here, the government introduced a Certificate of Non-Existence to prove that no such consent for Corona-Garcia's entry had been given following his deportation in December 1996. We have accepted similar certificates in the past to prove the absence of official permission to enter the United States. See United States v. Blanco-Gallegos, 188 F.3d 1072, 1075 (9th Cir.1999). Corona-Gareia does nothing to undermine the government’s proof in this regard. Corona-Gareia attempted to cast doubt on the Certificate's accuracy during cross-examination, and at oral argument, but on both occasions he was unable to minimize the fact that the Certificate clearly reflects the absence of any express consent on the part of the Attorney General for Corona-Gareia to reenter after he was deported in 1996. At most, his argument shows that the Certificate of Non-Existence fails to reflect Corona-Garcia’s 1988 request for permission to live legally in the United States. See Trial Tr. at 31-35, 41-44. This fact is irrelevant insofar as the Certificate of Non-Existence only purports to show (and was only offered to prove) the absence of any application made after Corona-Garcia’s 1996 deportation. See Trial Tr. at 27, 30, 31, 33. As a result, we confine our analysis to whether the government presented sufficient corroborative proof that Corona-Gareia entered the United States subsequent to this deportation.
. BLACK’S LAW DICTIONARY 344 (6th ed.1990), defines corroborate as “[t]o strengthen; to add weight or credibility to a thing by additional and confirming facts or evidence.”