"I don't have all the answers," said Draper. "But we know about suicide prevention and people who are more socially connected and have a sense of belief and self-worth and are valued at work and in their relationships are way more protected and generally happier people."
Post-traumatic stress disorder and associated mental health problems are to blame for many of the suicides among war veterans, according to Draper.
"The most important thing to remember is we can do something to stop this," said Draper, who, like Gresham, said that communication and support from others can help to prevent suicide.
Since 2001, more than two million service members have been deployed to wars in Iraq and Afghanistan. The cost for treating veterans of all eras and conflicts is estimated at $48 billion, according to the Department of Veterans Affairs.
PTSD was not even recognized until after the Vietnam War, according to Gresham, who recognized at the onset of his government career in 2000 the importance of increasing the VA budget after predicting the staggering number of cases that were to follow. "I knew mental problems would exceed the physical," he said.
"I feel sorry for the younger soldiers," he said. "They are now married, got a wife and kids and suddenly come back and they can't find a job. These things all compound."
As for the Vietnam veterans, they found less support in the 1960s and 1970s, when they returned from combat service. "The older veterans don't trust the government and they don't go for help," said Gresham.
Unlike World War II soldiers who were hailed as heroes, these servicemen returned to "feel a bit outcast and rejected," according to Gresham, who sits on the Vietnam Veterans Foundation.
Many of that generation refused to acknowledge they had PTSD and are suffering the consequences later in life. "Believe me, we have a real problem," he said.
"These guys were the first generation not to trust the guys in the white coats, and they didn't trust the government," said Gresham. "A lot of the Viet vets with PTSD held it in.
"They didn't want to let their family know their dark secret. They wanted to be in the workforce and be productive like the generation of World War II, but they were not respected by society."
The VA in the 1970s was not responsive to the needs of these veterans, he said. "I've seen what has happened to a lot of these older vets."
At a town meeting in Los Angeles several years ago, Gresham said he told a group of Vietnam vets. "You know Hollywood was correct when they did the movie the 'Fourth of July' with Tom Cruise. The VA did a lousy job of taking care of vets."
But today, according to Gresham, "The VA has made "tremendous efforts to spend lots of money on [PTSD]," he said.
In 2007, the VA partnered with the Substance Abuse and Mental Health Services Administration (SAMHSA) to create a dedicated line manned by veterans on the National Suicide Lifeline.
The so-called Veterans Crisis Line has fielded more than 250,000 calls a year from veterans and active members of the military, according to Lifeline director Draper.
"It's a brilliant idea and it's saved taxpayers money and saved lives," he said.
Draper said it is too early to see the impact of this collaboration but predicts that CDC suicide numbers will eventually drop, at least among veterans.
Gresham, who was involved in the creation of the hotline, is also hopeful. "It's so much better for veterans to get help from other veterans," he said. "There is a strong bond."
"If you have suicide thoughts and there's another veteran on the line, you trust your brother, whether it's a man or a woman," he said. "If they have been in combat, there is someone who understands you."
"They didn't trust the VA for a long time and now the VA has its arms open," said Gresham. "They do very good work now. They understand the problem."
If you or a loved one are in emotional distress, please call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255). We are here to help 24/7. You are not alone. Help is available. Veterans should press option 1.