Veterans with other-than-honorable discharges do not qualify for benefits like disability compensation, education assistance and military burials. Their job prospects and careers suffer. Mr. Shepherd, who won the Bronze Star for valor, had a breakdown, he said, after seeing his platoon leader killed. He refused to go on patrol because he was sick, he says, not shirking his duty.

The Yale students found that more than 250,000 Vietnam-era veterans had other-than-honorable discharges, and thousands probably had PTSD. What the plaintiffs are seeking seems only fair — that the military adopt “consistent and medically appropriate standards” to consider PTSD when reviewing discharges. “I want that honorable,” Mr. Shepherd said. “I did do my part.”