Thompson told 60 Minutes he heard voices in his head that night.
"You thought people were after you," Logan remarked.
"Yes," he replied.
And then in chilling detail, he described exactly how he killed Brenda Lane.
"She got into the front seat driver's seat. And I had the knife on her. And I sat in the back seat. And…," Thompson said.
"You jumped in the car and pulled a knife on her?" Logan asked.
"Yeah. Uh-huh," Thompson acknowledged. "Knife was already out. It was a butcher knife."
"She must have been scared," Logan remarked.
"Yeah, she was crying," Thompson said.
"She was terrified for her life," Logan said.
"I know. I know," Thompson replied.
Asked what he felt, Thompson said, "She knows she's going to die."
Why did he kill her?
"There was no reasoning at that point," Thompson said. "It was just get away."
"Tell me how it happened. Describe it for me," Logan asked.
"Just turned her around and she didn't move and I stabbed her four times," Thompson recalled. "I wanted her to die quickly."
Asked why he wanted her to die quickly, Thompson told Logan, "Not in pain. I didn't want her to be suffering in pain."
"You think if somebody stabbed you four times in the back you're not gonna suffer?" Logan asked.
"Not really, no," Thompson said.
"You know she was still alive when you drove away," Logan pointed out.
"I heard her scream," Thompson said.
Thompson managed to escape to Georgia but was arrested there after setting Brenda Lane's car on fire. Frankie Floied, an investigator in the case back in Tennessee, says it could have taken months to find the body if Thompson -- over the telephone - hadn't given such precise, intricate, directions to the place he killed her.
"What was going through your mind at the time when you were talking to him on the phone?" Logan asked Floied.
"How calm he was," the investigator remembered. "There was no remorse. There was no passion. It was just matter of fact. 'If you'll take, you take this road, this road, this road and this road.'"
"So exact," Logan remarked.
"It's like you telling me how to find a Frisbee that you've tossed and lost," Floied said.
"So what did that mean to you?" Logan asked.
"Cold, impassioned. Just a cruel person," Floied replied.
That was the picture prosecutors painted of Thompson at his trial. But it wasn't a complete picture, according to Thompson's current lawyers, Dana Chavis and Steve Kissinger, who are appealing his case. They say Thompson had severe mental problems dating back to his childhood and they are fighting to keep him alive.