By the very nature of the gravity of the case, defense lawyers and prosecutors spend far more time on a capital case than a noncapital one. It takes longer to pick a jury, longer for the state to present its case and longer for the defense to put on its witnesses. There are also considerably greater expenses for expert witnesses, including psychologists and, these days, DNA experts. Then come the defendant's appeals, which can be considerable, but are not the biggest cost of the case, prosecutors say.

Mr. Carlisle said his views on the death penalty had not been affected by the case of Bryan K. Uyesugi, a Xerox copy machine repairman who gunned down seven co-workers last November in the worst mass murder in Hawaii's history. Mr. Uyesugi was convicted in June and is serving life without chance of parole.

Mr. Carlisle has doubts about whether the death penalty is a deterrent. ''We haven't had the death penalty, but we have one of the lowest murder rates in the country,'' he said. The F.B.I.'s statistics for 1998, the last year for which the data is available, showed Hawaii's homicide rate was the fifth-lowest.

The homicide rate in North Dakota, which does not have the death penalty, was lower than the homicide rate in South Dakota, which does have it, according to F.B.I. statistics for 1998. Massachusetts, which abolished capital punishment in 1984, has a lower rate than Connecticut, which has six people on death row; the homicide rate in West Virginia is 30 percent below that of Virginia, which has one of the highest execution rates in the country.

Other factors affect homicide rates, of course, including unemployment and demographics, as well as the amount of money spent on police, prosecutors and prisons.

But the analysis by The Times found that the demographic profile of states with the death penalty is not far different from that of states without it. The poverty rate in states with the death penalty, as a whole, was 13.4 percent in 1990, compared with 11.4 percent in states without the death penalty.

Mr. Carlisle's predecessor in Honolulu, Keith M. Kaneshiro, agrees with him about deterrence. ''I don't think there's a proven study that says it's a deterrent,'' Mr. Kaneshiro said. Still, he said, he believed that execution was warranted for some crimes, like a contract killing or the slaying of a police officer. Twice while he was prosecuting attorney, Mr. Kaneshiro got a legislator to introduce a limited death penalty bill, but, he said, they went nowhere.