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Several Democrats objected, saying tobacco use among the military was twice the rate of the American population as a whole and that it was hurting readiness and increasing health expenses. They also said tobacco has been banned on Navy submarines without any problems.

Still, Mr. Hunter’s amendment easily passed with bipartisan support. He told The Washington Times on Thursday that he expects the amendment to remain in the bill as it advances to the House floor and eventually to a conference with the Senate.

Some Republicans said it was hypocritical of Democrats to want to restrict access to tobacco, which is legal, even as many of them voted last week to allow Department of Veterans Affairs doctors to prescribe medical marijuana in states where it’s legal — even though the drug is illegal under federal law. That marijuana amendment failed in the full House.

Democrats countered by saying it was hypocritical of Republicans to demand access to tobacco, even as they oppose government funds to be used to provide abortions for troops and their families at military hospitals overseas.

One amendment that didn’t succeed was a provision that would have granted citizenship rights to young adult illegal immigrants who agreed to join the military.

Several Republicans proposed attaching that to the defense bill, desperately seeking some immigration legislation they can pass this year. But they ran into opposition from the American Legion and retired military brass, who said it would politicize the defense bill and could jeopardize its passage.

Rep. Adam Smith of Washington, the ranking Democrat on the Armed Services Committee, did raise the proposal Wednesday night, but withdrew it.

Supporters could try to add it when the bill goes to the House floor.

The committee also rejected an effort to strip commanders of final say over prosecuting sexual assault cases, in an emotional debate over what all sides now agree is an epidemic within the military.

Some lawmakers had said military lawyers with experience handling the complex cases should have final say. But a narrow majority rejected that, saying the solution is to hold commanders responsible for their troops’ behavior and their own decisions.