“By lowering standards, we are endangering the rest of our armed forces and sending the wrong message to potential recruits across the country,” Mr. Meehan said. “Our men and women in uniform represent the best and brightest in America, and we need to keep it that way.”

Aaron Belkin, director of the Michael D. Palm Center, a research institute at the University of California, Santa Barbara, that focuses on the military’s “don’t ask, don’t tell” policy regarding homosexuality, obtained the most recent data from the Department of Defense.

Mr. Belkin said the increases in moral waivers in the Army posed a problem only to the extent that the military failed to track these recruits or provide special integration training for them.

Since more than 125,000 service members with criminal histories have joined the military in the last three years, Mr. Belkin said, “you have a sizeable population that has been incarcerated and is not used to the same cultural norms as everybody else.”

“The chance that one of those individuals is going to commit an atrocity or disobey an order is higher,” he said. “Many of those individuals can be good soldiers, but in some cases they have special needs. The military should address those needs rather than pretending they don’t exist.”

Recruiters ask potential recruits to reveal whether they have been arrested or convicted of crimes. City, county and state records are checked, as are federal fingerprint databases. The military searches for convictions but also looks at cases that were dismissed, dropped or settled in some way. If someone is found not guilty, depending on the crime, extenuating circumstances are explored, said Maj. Stewart Upton, a Defense Department spokesman.

The system is far from foolproof, though. Juvenile records can get tricky because of privacy laws; not every state will release sealed information. And if someone has moved to a different state, the criminal history may not always show up.