Lawmakers are pushing for several changes in how the U.S. military handles cases of reported sexual assault amid fresh data showing a sharp increase in the number of reported incidents.

Years-long attempts by lawmakers to revamp how the military investigates and adjudicates allegations of sexual misconduct got a jolt Tuesday when the Pentagon released data showing 3,374 recorded reports of sexual assault in 2012, compared with 3,192 the previous year, part of a 35 percent jump in related ­crimes over the past two years. Using anonymous surveys and sampling research as it has previously to better understand other personnel issues, the Defense Department also estimated that 26,000 personnel experienced “unwanted sexual contact” last year, a jump from about 19,300 in 2010.

Senate Majority Leader Harry M. Reid (D-Nev.) called on senators writing next year’s annual defense authorization bill to eliminate the ability of military commanders to reverse convictions for sexual assault under the Uniform Code of Military Justice.

In a letter to the Senate Armed Services Committee, Reid said that Congress “must hold commanding officers accountable and ensure that they establish a climate in which sexual assault is not tolerated.”

The Senate leader’s call to block a commander’s ability to overturn a conviction on sexual assault charges comes after two Air Force generals effectively pardoned officers accused of such crimes. Members from both parties in the House and Senate have proposed similar changes in recent days.

Reps. Mike Turner (R-Ohio) and Niki Tsongas (D-Mass.) introduced a measure Tuesday that would require any service member found guilty of rape, sexual assault, forcible sodomy or attempts to commit any of those acts to be dismissed or dishonorably discharged.

The proposal, known as the Better Enforcement for Sexual Assault Free Environments Act of 2013, also would bar any military officer from changing or dismissing a court-martial conviction in major cases, including sexual assault.

In the Senate, four women are leading the push for reform.

Sens. Kirsten Gillibrand (D-N.Y.) and Barbara Boxer (D-Calif.) plan to introduce a bill next week that also would strip military officers of the ability to change or dismiss charges and would remove decision-making power on sexual assault cases from the military chain of command. Instead, experienced military lawyers would determine whether ­cases of sexual assault go to trial and whether they go to a special or general court-martial. The chiefs of staff of the military services would have the authority to establish courts, empanel juries and pick judges to hear the cases.

Gillibrand chaired a hearing in March that included testimony from three former service members who were the first military victims of sexual assault to testify before the first Senate hearing on sexual assault in the ranks in nearly a decade.

Calling the new Pentagon findings “unacceptable,” Gillibrand said she is worried that 47 percent of enlisted service members said they fear retaliation for reporting ­cases of sexual assault.

A separate proposal by Sens. Kelly Ayotte (R-N.H.) and Patty Murray (D-Wash.) would provide military lawyers throughout any legal process to victims of sexual assault; expand the Pentagon’s sexual-assault-prevention team to better investigate cases; refer accusations of sexual assault to the general court-martial level or a more senior military official if there is a conflict within the chain of command; and bar sexual conduct between military instructors and trainees during and within 30 days of the completion of training programs.

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