“It could be very easy for the Taliban to say all the things that we want to hear in order to get us down to a zero or a very low troop presence,” said Jeremy Butler, a former Navy officer who runs the veterans service organization Iraq and Afghanistan Veterans of America (IAVA). “Probably with the assumption that the U.S. and the president would be not particularly inclined to reinvest servicemen and women back into the country.”

A third of IAVA’s veteran members deployed to Afghanistan at least once, according to Butler, and some have five or more combat deployments there. Many of the veterans he spoke with in recent days were especially concerned that the peace deal was signed before the Afghan government had agreed on how to share power with the Taliban after U.S. forces leave. “We want to end the engagement in Afghanistan,” Butler said. “We just want it to be done the right way.”

There’s been a growing consensus among veterans groups in Washington that a full withdrawal of U.S. forces from Afghanistan is long overdue. Last year, Concerned Veterans for America, a conservative advocacy group, made ending the post-Sept. 11 wars a legislative priority — a policy agenda it shared with more progressive veterans groups on the left, like VoteVets and Common Defense.

“Anecdotally, when you talk to veterans and service members about going to Afghanistan again and again and again, the response that you get is that people are tired,” said Nate Anderson, the executive director of Concerned Veterans for America. “People are tired of fighting this war that has no clear objective and that has no end in sight.”

Anderson, who deployed twice to Afghanistan as a Green Beret, added that the agreement signed over the weekend was a step in the right direction, but he added that the deal should not be considered a substitute to a full withdrawal of American forces from the country.

For other veterans, the idea of negotiating with the Taliban was unsettling, given the group’s history of human rights abuses. Lydia Davey, a former Marine who served in Afghanistan in 2005 and 2006, said she was ambivalent when she first heard the news, but then she thought more about the stories about life under the Taliban. Davey recalled one of her Afghan colleagues telling her that he had been arrested and beaten with electrical cords after the Taliban raided a wedding and arrested all of the men for listening to secular music at the reception.