HOUSTON -- The U.S. Supreme Court has refused to consider an appeal from a man sent to Texas death row for strangling and trying to rape a woman jogging on a trail near her Houston home nearly 17 years ago.

Arthur Lee Burton had appealed a lower court's rejection of his claims that his admission to a prison sociologist that he killed 48-year-old Nancy Adleman was improperly obtained and shouldn't have been used against him. The Texas Court of Criminal Appeals in 2001 threw out his original sentence. A new punishment trial was held the following year.

The 44-year-old Burton also had argued his legal help at his trial and in earlier appeals was deficient.

Evidence showed Adleman, a mother of three, was strangled with one of her own shoe laces.

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