NEW YORK -- Each time mental illness is cited as a possible factor in a high-profile mass killing in the United States, there's a collective sigh among mental health professionals here. Even as they see an opportunity for serious discussions of problems and remedies, they also worry about setbacks to their efforts to destigmatize mental illness.

"Most people who suffer from mental illness are not violent, and most violent acts are committed by people who are not mentally ill," said Dr. Renee Binder, president of the American Psychiatric Association.

If, hypothetically, everyone with mental illness were locked up, "you might think you were safe, but you are not," Binder said.

According to the National Institute of Mental Health's latest estimate, from 2012, there were an estimated 9.6 million adults in the U.S. -- 4.1 per cent of the total adult population -- experiencing serious mental illness over the previous year.

"If you look at that large pool of people, only a tiny proportion of them will eventually commit violence," Binder said. "How are you going to identify them? It's like a needle in a haystack."

Yet public perceptions can be hard to shake. Of the mass shootings of the past 10 years that are most ingrained in America's psyche, the mental health problems of the perpetrator became a central part of the narrative in several cases -- notably the rampages at Virginia Tech University in 2007, which left 33 dead, at Sandy Hook Elementary School in Connecticut, in which 20 children and six adults were killed, in a Colorado movie theatre in 2012, where 12 people were killed, and near the University of California, Santa Barbara, in 2014 that left six students dead.

Just this month, a jury convicted James Holmes in the Colorado massacre, after a wrenching trial that delved deeply into his mental problems.

In two rampages recently, the perpetrators also have been described as mentally troubled. After the killing of four Marines and a Navy sailor at a military facility in Tennessee, the family of slain assailant Muhammad Abdulazeez said he had been in and out of treatment for depression starting as an adolescent. John Russell Houser, who killed two people and wounded nine before killing himself at a Louisiana movie theatre last week, had a history of mental health issues; at one point a judge ordered him involuntarily committed to receive psychiatric care.

While these incidents seize public attention, there's far less focus on the serious, systemic problems besetting America's mental health system, says Jeffrey Swanson, a professor of psychiatry at Duke University School of Medicine.

"Forty per cent of people with serious mental illness are going without treatment -- our systems are fragmented and overburdened," Swanson said. "When do we pay attention to this? We pay attention when there's a horrifying mass casualty shooting, and then people say: Let's fix the system."'

That puts mental health professionals in a bind, Swanson said.

"We're trying to debunk the stigma that people in the mental health system are dangerous, and yet refocus attention to how do we improve the system," he said.

Swanson and many of his colleagues, while committed to combatting stigma, acknowledge that some people with serious mental illness are more likely to commit violence than people who are not mentally ill.

"There's a long way to go in developing treatment that works for more people," he said. "It's not just about getting better medications -- it's about providing the supportive services, jobs, access to housing."

Swanson has been working with other researchers and mental health professionals on steps that could be taken to reduce access to firearms by people who pose a high risk of violence -- whether or not those people have mental illness. By broadening firearms bans to include people who've been convicted of violent misdemeanours or domestic violence, Swanson believes public safety could be enhanced while avoiding further stigmatization of mental illness.

Another topic of concern pertains to sharing of information. After some of the recent mass killings, there were accounts of mental health professionals becoming aware that the eventual perpetrator might pose a threat, and questions about whether such information could be shared more effectively.

Binder says early intervention can be crucial in enabling a person to get proper mental health treatment before problems get out of control. To this end, his organization has presented a program in more than 2,000 schools across the U.S. that aims to train teachers to notice early warning signs and, if warranted, make referrals.

Paul Gionfriddo, CEO of the advocacy group Mental Health America, says school officials and other adults should think carefully about how to respond when young people do exhibit behavioural problems and avoid isolating them further.

"What these kids need is even greater socialization at this time in their lives," Gionfriddo said.