In one Supreme Court appeal, McCann said instructions to jurors deciding Hughes' punishment were not adequate. In another, the attorney contended new evidence showed Hughes was sexually abused as a child and a jury should be allowed to consider that at a new punishment trial.
Ellis McCullough, one of Hughes' trial lawyers, said this week he was convinced no evidence was planted or mishandled.
He said Hughes, brought to a police station for interviews in the early morning hours after the slayings, made phone calls from the police interrogation room to acquaintances, including his probation officer, that "were pretty devastating taken as a whole."
Evidence examined for DNA testing after his conviction and at his request found traces of Charles' blood on Hughes' clothing. At his trial, prosecutors showed Charles' glasses were found on a couch in his apartment. Hughes, who knew Charles through a friend, said police took the evidence from the crime scene, planted it in his apartment, illegally searched the place, coerced his confessions and copied his signature to them from another document.
"The fact is I didn't kill anyone," he told The Associated Press last month, speaking from a small visiting cage outside death row.
Hughes also denied the sexual assault conviction that resulted in his probation.
"I didn't know she was 13 at the time," he told the AP of the victim in that case. "I was led to believe she was 17."
Hughes moved to Houston in 1983 from his native Buffalo, N.Y., where a rape charge against him was dismissed when the victim failed to appear in court.
He testified at his capital murder trial that he pulled a knife on "a guy who came up to me from behind" and "stuck him twice" but denied it was the 3-year-old boy or Charles.
"I didn't stab anybody," he said. "Stabbing and stuck is two different things."