10 U.S.C. § 950f would provide:
(a) Review by United States Court of Appeals for the Armed Forces- (1) Subject to the provisions of this subsection, the United States Court of Appeals for the Armed Forces shall have exclusive jurisdiction to determine the final validity of any judgment rendered by a military commission under this chapter.
(2) In any case referred to it pursuant to section 950c(a) of this title, the United States Court of Appeals for the Armed Forces may act only with respect to the findings and sentence as approved by the convening authority. It may affirm only such findings of guilty, and the sentence or such part or amount of the sentence, as it finds correct in law and fact and determines, on the basis of the entire record, should be approved. In considering the record, it may weigh the evidence, judge the credibility of witnesses, and determine controverted questions of fact, recognizing that the trial court saw and heard the witnesses.
(3) If the United States Court of Appeals for the Armed Forces sets aside the findings and sentence, it may, except where the setting aside is based on lack of sufficient evidence in the record to support the findings, order a rehearing. If it sets aside the findings and sentence and does not order a rehearing, it shall order that the charges be dismissed.
(b) Review by Supreme Court- The Supreme Court of the United States may review by writ of certiorari pursuant to section 1257 of title 28 the final judgment of the United States Court of Appeals for the Armed Forces in a determination under subsection (a).