Here is the NIMJ amicus brief in support of the Petition for Certiorari in Akbar v. United States, No. 15-1257. The general theme of the brief is that “in contrast to  civilian criminal convictions, Congress specifically intended for [the Supreme] Court to take a more active role in supervising military convictions on direct appeal.” Brief at 18.
From the Summary of the Argument:
The Petition raises a substantial constitutional challenge to a death sentence; the Court of Appeals held that only this Court could properly resolve the question presented; and if this Court answers that question in Petitioner’s favor, it would raise doubt about the entire scheme by which the military justice system currently imposes capital punishment. It is hard to imagine how a servicemember could ever present a more compelling petition for certiorari than the Petitioner in this case. . . .
In the military context, collateral review of criminal convictions is severely limited to whether the military court gave “full and fair consideration” to the defendant’s constitutional claims. And unlike what’s true for civilian criminal convictions, Congress has clearly and explicitly indicated its desire for this Court to exercise a more aggressive supervisory role over military convictions—even though few, if any, will give rise to divisions of authority among the lower courts. Accordingly, while the Supreme Court is certainly not bound to exercise certiorari jurisdiction over military appeals in any or even most cases, the Court is meant to—and should—play a different and more active role in reviewing direct appeals from the military justice system. And whatever force that argument carries in the ordinary military criminal case, it should have especial significance here. . . .
Thus, Petitioner presents a substantial constitutional challenge to a death sentence—and to the current regime for capital sentencing in the military justice system, writ large—that can be resolved only by this Court on a direct appeal. If this Court is ever going to grant a servicemember’s request for plenary review of a conviction by court-martial, it should grant the Petition.
Brief at 2-4.