He vowed not to be taken alive. He told negotiators where he wanted to be buried. He fired several shots at police.

"I'm gonna die, I'm gonna die," Lamar Smith shouted during a nine-hour standoff Jan. 8 at an apartment building in North Point Breeze, according to witnesses.

In the end, the 29-year-old Mr. Smith did die, after a sharpshooter's bullet struck him in the chest. At that moment, he was moving toward SWAT officers with two guns in his hands, police said after the incident.

The Allegheny County district attorney's office is still investigating what happened, but one expert described Mr. Smith's death as a likely example of "suicide by cop."

"He fired at police. That's an attempted homicide on a police officer. That's serious stuff," said Kris Mohandie, a police and forensic psychologist based in Pasadena, Calif. "He's creating the end of his story."

It also has become an increasingly common way of ending one's life, according to a study organized by Dr. Mohandie and published this month in the Journal of Forensic Sciences.

After Dr. Mohandie and a team of researchers looked closely at 707 officer-involved shootings that occurred across North America from 1998 to 2006, they determined that 256 cases, or 36 percent of the total, involved people who were trying to be killed by police.

"I was blown away. I expected about 20 percent," said Dr. Mohandie, who has worked as a consultant for the Los Angeles Police Department.

Earlier studies did find lower percentages, but this new research encompasses a far larger number of cases, he said. Investigators also have become better at recognizing suicide-by-cop situations, taking note of a person's past suicidal behavior, psychological history, substance abuse patterns and relationship problems before they encounter police.

According to Dr. Mohandie's study, 95 percent of the people involved were male and 80 percent were armed during the incidents, the majority of them with guns. Ninety percent took some form of aggressive action against police, and 51 percent were killed during the confrontations.

The vast majority of the incidents were unplanned, but most did involve some type of "suicidal communications." Slightly more than 60 percent of the people involved had a history of mental health problems.

Dr. Mohandie said the study demonstrates the critical importance of enhanced training for officers on how to deal with someone who is contemplating suicide. But it also shows that, in some instances, there is a limit to what law enforcement can do.

"They were already suicidal and encountered police," Dr. Mohandie said. "That was the final straw. They say, 'I'm not going in. Kill me.' "

Since the beginning of the year, police in the region have shot and killed four people, including Mr. Smith. At least two had threatened to harm themselves, and all four had histories of mental health troubles or substance abuse.

Paul Palmer, 31, was shot on Feb. 3 on the North Side after he pointed a gun at an officer. On Feb. 15, state police in Greensburg shot and killed Joe Briggs, a 22-year-old Seton Hill University student who had threatened his roommates and himself and fired shots into the street. Christopher Winston, 37, was shot by police during a home invasion on Feb. 19 in Duquesne after he lunged at an officer who had ordered him to drop to the floor.

Local law enforcement officials won't characterize any of the shootings as suicide at the hands of police officers. But they said they recognize the difficulties in dealing with people who are potentially suicidal.

All Pennsylvania police recruits receive basic instruction on how to identify a person with mental health problems, and officials in Allegheny County are now trying to go further.

Three years ago, representatives from the Pittsburgh Police Bureau and the county Department of Human Services worked together to create the Crisis Intervention Team program, which trains officers to help troubled individuals connect with behavioral health services.

The program already has trained 70 Pittsburgh police officers and 17 suburban officers, according to Amy Kroll, director of the county's Office of Justice Related Services.

City police also place a heavy emphasis on training negotiators, Deputy Chief Paul Donaldson said.

"Effective communication skills are important in any interaction, but this is especially true in dealing with a mentally ill person in crisis," he said in an e-mail message.

Negotiations played a central role in the North Point Breeze standoff with Mr. Smith, who barricaded himself in an apartment when an argument with his girlfriend and her father led to a call to police.

At the time, Mr. Smith already had a troubled history: convictions for drugs, assault, robbery and firearms violations and a sentence served at SCI Graterford.

In one case in 1998 in Penn Hills, Mr. Smith was accused of grabbing a woman, choking her, punching her in the head and dragging her down the street by her shirt, according to a police affidavit.

During the January standoff, Mr. Smith would crank up his music and pace furiously around the apartment, sticking his head out the window at times. SWAT officers and a three-member negotiation tried to talk him into surrendering.

Mr. Smith fired one shot inside the apartment, not far from where officers were huddled. When he tried to jump out a window while holding guns, SWAT officers shot rubber bullets at him, striking him and forcing him back inside. They also launched pepper spray into the apartment.

Mr. Smith spoke on a cell phone with his relatives throughout the standoff and agreed to surrender at least twice, police said, but he changed his mind.

A sniper in an adjacent building fired the fatal shot at Mr. Smith.

"They managed it the best it could be managed," said Elizabeth Pittinger, executive director of the Citizen Police Review Board, which handles civilian complaints about the police bureau.

"Public safety was protected. They possibly saved other lives that day."

Police officers, she said, "never go out to kill anybody. But they're prepared to do so if that's what it takes to protect everybody else. Some people know that, and they're ready to exploit it."

According to Dr. Mohandie's study, most "suicide-by-cop" encounters end much faster than the North Point Breeze standoff. More than 70 percent of the incidents his team examined took place in less than an hour, and 29 percent were over within 10 minutes.

In such rapidly evolving situations, often the responding patrol officers have to take action before the arrival of SWAT officers or negotiators.

The two other officer-involved shootings in Allegheny County this year happened after just minutes, not hours.

At the time of his death, Mr. Winston already had received treatment at Mayview State Hospital for mental disabilities and he had served two prison sentences.

The first followed a 1993 attack on his 7-month-old son, who was taken to Children's Hospital with bite marks and bruising on his face and shoulder, according to court records. Mr. Winston pleaded guilty to aggravated assault and endangering the welfare of a child.

In 2001, Mr. Winston broke into the North Side house of his girlfriend's father, Robert Blackwell. He hit Mr. Blackwell in the head with a hammer, fracturing his skull. He also "body-slammed" a woman outside on the street, court records said.

Mr. Blackwell, 60, a baker, said he had no idea what pushed Mr. Winston to attack him. Mr. Winston eventually surrendered to police.

Dr. Christine Martone of the Allegheny County Behavior Clinic later told a judge that Mr. Winston was "severely mentally disabled."

During the Duquesne incident last month, Mr. Winston appeared to be trying to hurt a woman who lived in the house in the 600 block of South 5th Street. Even after an officer shot him, he fought back.

"I just think he had a lot of troubles and it escalated," county Police Superintendent Charles Moffatt said.

Few suicide-by-cop cases involve a person with a plan to die, according to Dr. Mohandie: "None of the guys that did this woke up and said, 'This is the day the police are going to shoot me.'"

The motives for such suicides vary.

Some people see themselves as victims and want to lash out against society. Michael McLendon, the gunman who killed 10 people and himself last week during a shooting rampage in Alabama, harbored resentments over his failure to become a Marine or a police officer and kept a list of names of people he believed had wronged him. He shot and killed himself after being cornered by police.

Others are driven by narcissism or machismo and want to die in a "blaze of glory," Dr. Mohandie said.

A few even choose this route to death because suicide at their own hands is prohibited by their religious beliefs, he said.

Yet there's often ambivalence among many suicidal people, and police officers can, and do, bring some back from the brink.

Ross police Sgt. William Barrett, a negotiator with the North Hills special response team, recently talked a woman out of shooting herself after she had already fired at a relative.

They communicated over the telephone for several hours.

"At first, you have to let the person talk," Sgt. Barrett said. "You're a sounding board. It's letting them know there are people who care and who are willing to listen to their situation."

Sgt. Barrett is one of 62 people who completed the new Applied Suicide Intervention Skills Training program, organized by Contact Pittsburgh and open to the public.

"Suicide is preventable," said Christy Stuber, executive director of Contact Pittsburgh, which operates the suicide hotline number 412-820-HELP. "We'd like to train people in the community, and police, to identify suicidal signs and then intervene."

Sgt. Barrett has also gone through the Crisis Intervention Team program, which he described as "some of the best training I've ever received" in 22 years as a police officer.

According to Allegheny County's Ms. Kroll, police have already brought more than 100 people to seek help at a South Side referral center for mental disabilities since the CIT program started.

Ms. Pittinger, of the police review board, said she would like to see city police officials encourage more officers to participate in the training. Eventually, she said, it should be mandatory for all officers.

"We have to get away from criminalizing mental illness," she said, "and law enforcement is finally on board with that."