More than 3,300 federal inmates have applied to have their prison sentences cut short in the months since the Justice Department rolled out a new clemency initiative, according to data.

That figure represents nearly five times the number of inmates, 702, who applied for sentence commutations during the same period last year, the department said.

The surge of petitions since late April followed the Justice Department’s announcement that it was broadening the criteria for inmates seeking clemency. The goal of the new cost-cutting initiative, officials have said, is to reduce the nation’s bulging prison population and grant leniency to nonviolent drug offenders sentenced to double-digit terms at the height of the 1980s-era crusade against crack cocaine.

The clemency effort is not limited to drug offenders, who make up about half of the roughly 216,000 federal prisoners, but its half-dozen criteria make clear that those inmates are the target population.

To be eligible, inmates must have already been behind bars for at least 10 years, have a nonviolent history, have no major criminal convictions, have a good behavior record in prison, and be serving a sentence that, if imposed today, would be substantially shorter than what they were given at the time.

“These older, stringent punishments that are out of line with sentences imposed under today’s laws erode people’s confidence in our criminal justice system,” Deputy Attorney General James Cole, the department’s second-ranking official, said in announcing the new criteria in April. Months earlier, he urged lawyers around the country to help drug prisoners prepare clemency petitions.

Officials had anticipated receiving thousands of additional applications, though the expectation has been that many of those seeking commutation would not meet the necessary criteria.

The Clemency Project 2014, a coalition of defense lawyer groups and prisoner advocates, said this week that more than 20,000 federal prisoners have returned surveys seeking to have a lawyer during the clemency process. That number includes some of the inmates who have already petitioned the Justice Department for clemency, the department said.

None of the petitions has yet been forwarded to President Barack Obama for his approval, though lawyers are in the process of reviewing the applications to see which ones have merit. It’s not clear how many of the petitions that have been received will fit the criteria.

Vanita Gupta, the deputy legal director for the American Civil Liberties Union, said the Justice Department appears to have embraced the idea of a rigorous clemency process after years of relative inactivity. President Barack Obama granted only one commutation during his first term, and in December commuted the sentences of eight people he said were serving unduly harsh sentences.

Gupta called the clemency announcement historic and unprecedented, even though no one knows many inmates will ultimately be affected.