SUMMARY ORDER
ON CONSIDERATION WHEREOF, IT IS HEREBY ORDERED, ADJUDGED, AND DECREED that the judgment of said District Court be and it hereby is AFFIRMED.
Defendant-appellant-cross-appellee Michael Baker (“Baker”) appeals from a final judgment of conviction and sentence imposed on March 28, 2005, by the United States District Court for the District of Vermont (Sessions, ./.). Baker was charged with conspiracy to distribute cocaine in violation of 21 U.S.C. §§§ 846, 841(a)(1), 841(b)(1)(B). We assume the parties’ familiarity with the facts, procedural history, and specification of issues on appeal.
On appeal, Baker challenges certain rulings of the district court made during his trial and sentence. Specifically, he argues that: (1) he was prejudiced by the government’s “[cjross [ejxamination of [ijrrelevant [mjatters,” see Defendant’s Br. at 1; (2) his testimony regarding his medical diagnoses was wrongfully excluded; (3) the district court erred in enhancing his sentence for obstruction of justice; (4) the district court erred in refusing to grant him two points for acceptance of responsibility; (5) the district court erred in determining that “the court could not go below the 60 month minimum even though Mr. Baker had already served 42 months in presentence confinement,” see Defendant’s Br. at 2. Each of these issues will be addressed in turn.
(1) Generally, all relevant information is admissible under the Federal Rules of Evidence, unless specifically excluded, and “[district courts have broad discretion to determine the relevancy of evidence.” United States v. Amuso, 21 F.3d 1251, 1262-63 (2d Cir.1994). This broad discretion extends to the district court’s control over the scope of cross examination. See United States v. Wilkerson, 361 F.3d 717, 734 (2d Cir.2004).
Effective cross examination is essential to elicit truth. United States v. Havens, *568446 U.S. 620, 627, 100 S.Ct. 1912, 64 L.Ed.2d 559 (1980). Thus, if the defendant takes the stand, his privilege against self incrimination does not shield him from proper questioning about matters testified to on direct examination. See id. “When a defendant offers an innocent explanation he ‘opens the door’ to questioning into the truth of his testimony, and the government is entitled to attack his credibility on cross-examination.” United States v. Payton, 159 F.3d 49, 58 (2d Cir.1998). In this situation, the government may cross examine a defendant as to the truth of matters discussed on direct even if they are unrelated to the merits of the charges against him. Id.
The district court did not abuse its discretion in ordering Baker to reveal from where he obtained the steroids that he testified to taking regularly. Because Baker testified on direct that his steroid usage prevented him from forming the requisite intent to participate in a cocaine conspiracy, questions attempting to discredit this story were directly relevant. In taking the stand on direct, Baker minimally opened the door to questions probing such testimony, at least insofar as they related to his credibility.
Where a defendant refuses to testify in such a situation, a district court may strike all of the direct examination that relates to matters about which the defendant refuses to testify to on cross examination, see United States v. Frank, 520 F.2d 1287, 1292 (2d Cir.1975). The district court in the instant case did not even go this far. Instead, it simply gave an instruction that the jury could infer that Baker’s refusal to answer the question may be considered in assessing his credibility and the weight given to his direct testimony on the matter. We cannot say that the district court abused its discretion in so instructing the jury in light of Baker’s, at least partial, waiver of his Fifth Amendment privilege.
(2) The district court did not abuse its discretion in excluding Baker’s testimony about his medical diagnoses. First, any testimony relating to Baker’s psychological condition was irrelevant to his defense of intoxication. Second, testimony relating to Baker’s substance-abuse diagnoses was hearsay if offered to prove that Baker had such a condition. See Fed.R.Evid. 801(c) (stating that evidence is inadmissible hearsay if uttered by an out-of-court declarant and offered for the truth of the matter asserted). On appeal, Baker also contends that the diagnoses were offered for other reasons, but insofar as these justifications were not offered below, they were waived. See United States v. Tarricone, 996 F.2d 1414, 1423 (2d Cir.1993). Therefore, given the deference we accord rulings on evidentiary issues such as hearsay, we cannot conclude that the court abused its discretion in excluding Baker’s testimony about his diagnoses.
(3) In increasing Baker’s sentencing level for obstruction of justice, the court explained that it found the increase warranted because Baker thwarted the government’s attempt to impeach him by refusing to answer a question directly relevant to direct examination, despite the court’s instruction for him to do so.
A sentencing judge may enhance a defendant’s sentence for obstruction of justice under U.S.S.G. § 3C1.1 if “the defendant willfully obstructed or impeded, or attempted to obstruct or impede, the administration of justice during the course of the investigation, prosecution, or sentencing,” and the obstruction related to any relevant conduct. Id. We give the sentencing court due deference in its application of the Guidelines to the facts. United States v. Cefalu, 85 F.3d 964, 968 (2d Cir.1996).
This Court has found such deference merited in another case similar to Baker’s — when a defendant refused to give *569handwriting samples despite being compelled by subpoena. United States v. Valdez, 16 F.3d 1324, 1335 (2d Cir.1994). In so finding, we explained that the defendant’s disguising of his handwriting hindered the government’s investigation and was a classic example of obstruction of justice. See id. Similarly, according the district court its due deference in the instant case, we find that Baker’s refusal to comply with a court directive — even after a determination that it would not violate Baker’s Fifth Amendment privilege against self incrimination to do so — enabled the district court to increase Baker’s range by two points for obstruction of justice.
(4) “A district court’s refusal to depart downward is generally unreviewable on appeal, unless its action falls within a few narrow exceptions to the general rule.” United States v. Duverge Perez, 295 F.3d 249, 255 (2d Cir.2002) (internal citation omitted) (emphasis added). The primary exception recognized is when the district court mistakenly believes that it lacks the authority to depart downward. Id.
The district court did not misapprehend its authority to depart downward from the applicable Guidelines range. Indeed, the court substantially departed downward from the range that it found applicable. We therefore affirm the court’s refusal to depart downward for acceptance of responsibility.
(5) Baker contends that the district court erroneously concluded that it could not impose a sentence less than sixty months because of the mandatory minimum imposed by 21 U.S.C. § 841(b)(1)(B)(ii)(II), however, we do not find this to be so. Moreover, the district court did credit Baker for time served in accordance with his state sentence. In fact, the court expressly stated that it was reducing Baker’s sentence by forty-eight months for time served in state custody, pursuant to U.S.S.G. § 5G1.3(e). After crediting Baker for time served, the court then sentenced Baker at the low end of the Guidelines range. Additionally, the court stated that after pondering Baker’s case, it had come to the conclusion that the sentence was fair and just, and thus it was the sentence that the court would have chosen to impose, all things considered. We therefore reject Baker’s arguments to the contrary.
ON CONSIDERATION WHEREOF, IT IS HEREBY ORDERED, ADJUDGED, AND DECREED that the judgment of said District Court be and it hereby is AFFIRMED.
Accordingly, for the reasons set forth above, the judgment of the District Court is hereby AFFIRMED.