State attorneys have said the racial reference during Buck's sentencing phase was a small part of larger testimony about prison populations. In Texas, jurors must decide on the future danger of an offender when they are considering a death sentence.
Two years ago, Buck was within a six-hour period set for his execution when the U.S. Supreme Court gave him a reprieve. The high court decided months later not to review his case and lifted the reprieve, and the justices have refused a request from Buck's lawyers to reconsider that decision.
He does not now have an execution date.
Buck was convicted of gunning down ex-girlfriend Debra Gardner, 32, and Kenneth Butler, 33, outside Houston on July, 30, 1995, a week after Buck and Gardner broke up.