Attorney William Sussman also argued that jurors should have been told that Mr. Arrington's roommate raped the victim, 46-year-old Kathy Lynn Hutchens, weeks before her murder. Mention of the rape was disallowed because the only evidence was a statement by Ms. Hutchens' sister about it, making it hearsay evidence.
Mr. Arrington was convicted in 2004 and given the death sentence for Ms. Hutchens' murder three years earlier. He had been released from prison for killing his wife 15 years before in a similar drunken rage, prosecutors say.
Mr. Sussman said the $1,500 allocated by Richmond County Superior Court Judge William M. Fleming wasn't enough to discover evidence that might be considered mitigating and could have persuaded the jury to give Mr. Arrington a lighter sentence.
"I think we should have been able to develop that evidence," Mr. Sussman said. "We should have, and it might have saved his life."
A special investigator was needed because people in the Harrisburg neighborhood where Mr. Arrington grew up were reluctant to talk to attorneys, Mr. Sussman said.
"There wasn't anybody in Augusta that was trained as a mitigation investigator," he said. "We could have trained one, but it would have been easier to bring one in from Atlanta."
Assistant District Attorney Charles Sheppard said there's no reason to believe a special investigator could have discovered useful evidence.
"In most cases like this, you can always find something helpful after the fact. You can go on infinitely showing there is some evidence that should have been presented," Mr. Sheppard said. "But the fact of the matter is there is nothing that has been revealed thus far to this court that could have had a major impact on this case that wasn't introduced at the mitigation or sentencing phase of this case."
The seven high court justices will take two or three months to consider Tuesday's arguments and hand down a decision.
Mr. Sussman submitted legal briefs outlining 20 mistakes he said were made in Mr. Arrington's trial. Prosecutors filed their own briefs denying all of them, and the justices could consider any of them in their decision as well.