Lawyers for a convicted killer on death row are asking New York's highest court to make it harder for prosecutors to win death sentences, just as some prosecutors are growing impatient with the court, which has yet to approve a single execution.

In written arguments in a death penalty case to be considered by the New York Court of Appeals on Wednesday, the state's Capital Defender Office argues for the first time that the state Constitution requires a special rule for death penalty cases. That rule would mean that to convict someone of capital murder, the standard of proof would be greater than "beyond a reasonable doubt," the standard for conviction in criminal cases in this country for centuries.

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In its place, the lawyers said, the court should require prosecutors to prove a defendant's guilt "beyond any doubt" to justify an execution. The proposal is opposed by prosecutors and is just one of scores of claims made on behalf of a death row inmate, Angel L. Mateo, who confessed in 1996 to four Rochester killings. Lawyers who follow the court say it is unlikely the judges will adopt the proposal in Mr. Mateo's case.

But experts on capital punishment say the fact that the proposal has reached New York's highest court reflects the shifting ground in legal battles over the death penalty nationally. Spurred by DNA exonerations, defense lawyers are increasingly tailoring arguments to take advantage of what they see as growing public concern about the possibility that innocent people might be put to death.

The idea of increasing the level of certainty required for conviction is one of a handful of proposals to modify capital punishment that have gained attention around the country in the last few years. Some of its proponents are death penalty supporters who say the only way to shore up public support for execution is to try to ensure that only those who clearly deserve the ultimate punishment are put to death.

"I am certainly no shrinking civil libertarian," Frank Keating, a Republican and the former governor of Oklahoma, said in an interview, "but I think if you're going to take somebody else's life, you need to be convinced to a moral certainty."

Mr. Keating, who was also a senior Justice Department official in the Reagan administration, unsuccessfully sought to change Oklahoma's death penalty law to require proof "to a moral certainty" while he was governor in 2001.

James S. Liebman, a Columbia Law School professor who has written widely on the death penalty, said the proposal to increase the standard of proof in death penalty cases has been endorsed by some influential criminal law experts since the 1960's. He said the idea, which he favors, "is a very logical outgrowth of the view that we can have a death penalty and make it reliable."

But some prosecutors say the proposal would block all death penalty cases because it is not possible to remove all doubt. "Even if the crime was committed on videotape, somebody could always come up with a doubt," said the district attorney in Schenectady, Robert M. Carney.

The district attorney in Utica and the president of the New York State District Attorneys Association, Michael A. Arcuri, said, "If that standard is adopted, we will not have a death penalty in New York."

Still, some lawyers say changes in the law are often won in incremental battles that can take many years. Eric M. Freedman, a Hofstra University law professor who has worked on death penalty cases, said the proposal to increase the standard of proof could become more persuasive as court battles unfold. "Arguments gain traction in the legal system over time," he said.

This is not the first time similar arguments have reached courts around the country. In a dissent in a death penalty case in 2002, a New Jersey Supreme Court justice, James H. Coleman Jr., said there was a special need for reliability in capital cases. He said some facts in the cases should be proved to a degree greater than "beyond a reasonable doubt." The same standard "used to determine whether an individual should be found guilty or innocent of possession of a marijuana cigarette," he wrote, "should not be used in determining whether an accused can be executed."

As in many debates about the death penalty, proponents of raising the legal standard differ on how it should be done. Robert Blecker, a professor at New York Law School who favors capital punishment, said one problem with current law is that it makes jurors' decisions about whether to impose death formulaic, leading to accusations that too many people are sentenced to death.

He said it was important that prosecutors should prove person guilty of a murder charge by the traditional "reasonable doubt" standard. To raise the standard in that part of a capital case, he said, would make convictions impossible.

But Mr. Blecker, who is writing a book arguing in favor of the death penalty, said that when jurors then determine whether to sentence someone to death, they should be required to meet a higher standard. He said the standard should be proof to a moral certainty that a defendant deserves to die.

That, he said, would return credibility to the death penalty by ensuring that only "the worst of the worst" are sent to death row. Currently, he said, the law permits jurors to impose death too freely. "The law," he said, "should require you to be angry enough at the defendant to want him to die."

The Court of Appeals has already reviewed two death sentences since New York's death penalty law took effect in 1995. It overturned both sentences on narrow grounds. Lawyers who have watched the court say they consider a similar ruling likely in the case of Mr. Mateo, who was sentenced to death for one of the four murders.

In a confession, he wrote, "I think I should get the death penalty for the things I did."