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A convicted New York cop killer is hoping to avoid the death penalty by using an increasingly common defense - he's just not smart enough to face execution for his crimes.

Lawyers for Ronell Wilson began trying to convince a federal judge on Monday to uphold an appeals court's decision to overturn the death sentence for the 2003 murder of New York City detectives Rodney Andrews and James Nemorin during an undercover sting in the borough of Staten Island. With an IQ of just under 70, defense attorneys say Wilson is mildly retarded and therefore exempt from the ultimate punishment.

Experts say the argument increasingly has been made on behalf of death row inmates since a 2002 U.S. Supreme Court ruling, in Atkins v. Virginia, that held executing mentally retarded individuals violates the Eighth Amendment ban on cruel and unusual punishments. In a procedure that is expected to last three weeks, the judge will likely examine Wilson’s complete educational history, as well as a formal IQ score and adaptive function tests. If he scores low enough, it could save his life.

“That’s half the battle, that you can show a mental history for the court to make a determination,” N. G. Berrill, a forensic psychology professor from John Jay College in New York, told FoxNews.com.

But Berrill said prosecutors may be able to show Wilson was smart enough to function - and to know right from wrong.

“Someone may have a low IQ but have high ‘street smarts,’ and these things might reveal another level of intelligence,” he said.

Wilson is the latest of many killers to employ the low IQ defense, also known as the Atkins defense.

In August, Marvin Wilson, a Texas man who was convicted of killing a police informant, was executed after it was determined that he was mentally competent for his death sentence to stand. Attorneys for Wilson used the defense when they referred to a 2004 psychological test that showed his IQ registering at 61, which is below the minimum standard of 70.

Prosecutors countered, saying that the claim was supported by only one test, which leaves room for error. The Supreme Court agreed and his request was denied a mere two hours before his execution was carried out by lethal injection.

Also in August, the death sentence of a U.S. Marine was overturned despite his Atkins defense being overruled by the court.

The Navy-Marine Corps Court of Criminal Appeals cited many problems in the original criminal trial of Lance Cpl. Kenneth Parker, whose sentence was reduced to life in prison as a result.

Parker was originally charged for shooting a fellow Marine to death in March 1992 after a night of drinking with friends led to a racially charged discussion, stemming from rumors a white Marine had attempted to lynch a black person on Martin Luther King Jr’s birthday.

Parker and five other African-American Marines “vowed revenge" and picked a random target in Jacksonville, N.C., where Parker shot Lance Cpl. Rodney Page with a 12-gauge shotgun that he used a few days later in another murder.

An appellate court had rejected the argument by Parker’s defense that a combination of a below-average IQ and heavy drinking left him incapable of criminal intent.

As for Wilson, experts said the brutality of the murder of the two New York City detectives is not what is at issue.

“This was a brutal murder, and it raises tremendous outrage and demands that it is treated with the greatest sanction," Alan Lipman, a behavioral sciences professor at George Washington University Medical Center and director of the Center for the Study of Violence, told FoxNews.com. "The question here is whether being mentally retarded is the difference between the death penalty and life in prison.

“He is right on the line, which means that [a ruling] could go either way. The judge has set aside three weeks for this hearing, which says to me that he knows there will be lengthy arguments from both sides. This is going to be a close call.”