HOUSTON  Bobby Wayne Woods was executed Thursday evening in Texas after his lawyers lost a battle to persuade the courts that he was too mentally impaired to qualify for capital punishment.

Mr. Woods, 44, was convicted of raping and killing an 11-year-old girl in 1997. He received a lethal injection and was pronounced dead at 6:48 p.m. in the death chamber at a state prison in Huntsville, Tex., after the United States Supreme Court denied a request from his lawyers to stay his execution. His last words, at 6:40, were: “Bye. I am ready.”

Tests administered to Mr. Woods over the years placed his I.Q. between 68 and 86, prompting a bitter debate between his lawyers and the state over whether he was too impaired to face execution. The state and federal courts repeatedly sided with prosecutors.

The debate reflects the gray area left by the Supreme Court in 2002, when it ruled that the mentally impaired were not eligible for the death penalty but left it up to state courts to interpret which inmates qualified as impaired.