HOUSTON (CBSDFW.COM/AP) — A prisoner on Texas death row for dragging a black man to death behind a pickup truck more than two decades ago is one step closer to execution after the U.S. Supreme Court turned down his appeal.

The high court on Monday denied without comment 43-year-old John William King’s appeal. He claimed he had ineffective lawyers at trial.

A photo of James Byrd Jr., the Texas man dragged to his death in Jasper in 1998. (credit: CBSDFW.COM)

Additionally, King’s appeal said that only a few pieces of circumstantial evidence that could be innocently explained tied him to the scene of a fight that resulted in the death of James Byrd Jr.

The 49-year-old was chained at his ankles to the bumper of a truck in June 1998 and fatally dragged outside Jasper, about 125 miles northeast of Houston.

Painted circles that marked evidence in the dragging death of James Byrd Jr., visible on the county road outside Jasper, Texas on January 27, 1999. (credit: Paul Buck/AFP/Getty Images)

What was left of his shredded remains was dumped between a black church and cemetery where the pavement ended on the remote road. Fingerprints taken from the headless torso identified Byrd.

King was sentenced to death for the brutal slaying.

One of two other white men convicted has been executed. The third is serving life.

Former Jasper County Sheriff Billy Rowles tells KFDM-TV the case is “nearing an end.”