BETTY ANN BOWSER: In 1992 George McFarland was tried, convicted and sentenced to die for the murder of a Houston convenience store owner. The trial lasted less than three days–and through much of it one of McFarland’s attorneys was asleep.

GEORGE McFARLAND: So I’m nudging him with my feet–what are you doing–wake up! So later that day I asked him I said: "Well what happened?" "Oh, I was just tired." And I asked him, I told him, I said, "Man, I’m fighting for my life here. You’re supposed to be helping me"–"Oh, I got it under control George." He always told me: "I got it under control."

BETTY ANN BOWSER: McFarland appealed his conviction to the Texas criminal court of appeals, citing, among other things, ineffective counsel. The appeals court said it "did not condone" the behavior of the attorney but ruled that because there was a second lawyer present during the trial McFarland failed "to make any showing that he was not effectively represented" added Congress in here.

Now McFarland wants to go into federal court to seek relief through habeas corpus–a legal term meaning he is alleging his constitutional rights have been violated. But under the anti-terrorism-Effective Death Penalty Act passed by Congress in 1996, it will be harder for him to do that because the new habeas corpus law places a time limit on death row inmate appeals ; streamlines the entire appellate process; and may limit inmates’ ability to appeal state court decisions in the federal system.

Before the new law, McFarland could make one appeal after another sometimes on the same issue. University of Houston Law Professor David Crump says the law is designed to do what is says–make the death penalty more effective.