HOUSTON (AP) — A Mexican man on Texas death row can move forward with an appeal focusing on whether his attorneys were deficient during the sentencing phase of his trial for strangling and raping a 16-year-old girl in Waco 31 years ago, a federal appeals court has ruled.

In the same ruling Tuesday, two of three judges on a 5th U.S. Circuit Court of Appeals panel rejected arguments that 64-year-old Ramiro Ibarra is mentally impaired and ineligible for execution. An earlier unsuccessful appeal argued Ibarra, who was in the U.S. illegally, should have received protections under an international treaty.

Ibarra was arrested in 1987 the day the body of Maria Zuniga, a family acquaintance, was found. He was released because of an improper search warrant and wasn't arrested again until 1996.

The 5th Circuit in 2012 ruled against his claim that attorneys failed to properly investigate and present evidence of Ibarra's extreme childhood poverty and physical and emotional abuse from his father and that the evidence could have convinced jurors to choose a life sentence rather than death. That ruling, however, came a year before a precedent-setting decision by the U.S. Supreme Court in a similar case involving deficient legal help for a Texas death row inmate.

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After his capital murder trial in Waco, Ibarra was convicted in nearby Bell County of sexually assaulting a nephew and received a life prison sentence.

In another capital case, the Texas Court of Criminal Appeals on Wednesday upheld the conviction and death sentence of Fidencio Valdez for a fatal shooting during a 2010 drug deal in El Paso.

Attorneys raised 13 points of error from his 2014 trial, including arguments that false evidence was presented, that evidence didn't support a capital murder conviction, that the jury charge and instructions were improper and his trial legal help was deficient. Valdez's lawyers also raised constitutional challenges.

Valdez, 39, was convicted and sentenced to death for the slaying of 18-year-old Julio Barrios. Authorities used phone records and DNA evidence to tie him to the killing.