States have begun relying more on such programs and reducing penalties, particularly for low-level drug offenses, in attempts to save money. Mr. Holder’s speech Monday, in which he acknowledged that “we cannot simply prosecute or incarcerate our way to becoming a safer nation,” underscores a shift in thinking at the federal level. The Bureau of Prisons budget doubled to nearly $7 billion last year from $3.6 billion in 2000.

“All you need to know is we’re spending $80 billion to house prisoners at the federal, state and local level. I can guarantee you these [diversion] programs don’t cost that much,” said André Birotte Jr., the U.S. attorney in Los Angeles, who has been testing a program known as Conviction and Sentence Alternative, or CASA, for about a year…

Today, more than 2,800 drug courts exist throughout the country, mostly in state systems, according to the National Institute of Drug Court Professionals. In the federal system, less than 1% of the more than 109,000 cases in 2012, the latest data available, were diverted into drug courts.

A 2011 study by the Urban Institute, a policy and research group, found that for every $1 spent on participation in such programs, $2 was saved. But the group said the findings weren’t statistically significant, because the majority of crimes were minor and would have led to relatively low-cost prison terms. The drug courts, the report said, could lead to significant savings, but only if they enroll serious offenders.