For years, rape kits piled up in Houston. Thousands and thousands of swaps, running back almost 30 years, sat untested. Victims heard nothing. Perpetrators went on with their lives and, in some cases, committed further crimes. Eventually, there were nearly 6,700 kits waiting to be processed.

Then, in 2013, Mayor Annise Parker launched a push to test the kits. The results are stunning: Tests turned up 850 matches in the FBI's national DNA database. Prosecutors have charged 29 people and obtained six convictions so far. Of course, the delay was costly: As the Harris County prosecutor noted, suspects in some cases committed other crimes, even as the untested kits that could have convicted them sat untested—including at least six further rapes. (Given a national backlog of rape kits, there might be even more.)

Houston's test result is good news, and it's the latest in a slow revolution in how authorities are handling rape kits. In 2014, Memphis, Tennessee, began moving to process a 12,000-kit backlog. An especially egregious case was Detroit, which discovered some 11,000 kits in an abandoned police facility in 2009 but has since begun an ambitious effort to solve the problem. While testing on those kits has proceeded slowly, it has already identified 100 serial rapists, according to prosecutors. In 2014, Michigan Governor Rick Snyder signed a law establishment timelines for rape-kit testing. Cleveland has sent 4,700 kits for testing. Las Vegas has 4,000. There's no definitive number, but estimates of the number of untested kits, nationwide, range from at least 100,000 to 400,000. Manhattan had a 17,000-kit backlog that it began clearing in 2000, yielding dozens of convictions as well as connections to other assaults in New York's other boroughs.

The problem, say advocates, is not just for the women and men who have been attacked and whose cases haven't been resolved. There's evidence of substantial rates of serial rape and of general serial criminality among rapists. When kits are not tested promptly, perpetrators are left at large to commit additional rapes that might have been prevented.

Investigators have often been reluctant to test in cases in which suspects are known to their accusers, choosing instead to test only kits from rapes perpetrated by strangers, said Linda Fairstein, a former New York sex-crimes prosecutor who's now on the board of the Joyful Heart Foundation, a nonprofit that works toward rape-kit reform. Investigators might not bother testing a kit in a domestic violence case, for example. Testing when DNA evidence wasn't necessary to secure a conviction seemed like a waste of time and money, and the public got most panicked about rapes by strangers.

But that's only a superficial tradeoff, Fairstein said, since someone who raped an acquaintance may well have other victims. Moving faster to test kits can actually be an effective way of preventing crime both in the city that holds them—as Houston's experience demonstrates—and to protect other jurisdictions.

"By spending a significant amount of money, you are identifying the most violent offenders that we have and you're preventing more crimes from occurring," Fairstein said. "It's really rare that you're going to come up with the single-rapist event. You'll find many of these guys in prison, you'll find them across state lines."

One common complaint is that there simply isn't the money—$500 to $1,000 per kit—to process so many kits. That's particularly disheartening in light of the billions spent on criminal justice in the U.S. every year. But where federal and local money are failing, other sources are starting to deliver. In addition to groups like Joyful Heart, there are more and more sources of funding. Manhattan District Attorney Cy Vance Jr. announced a program in November to use money seized via asset forfeiture to create grants for other cities to clear their backlogs. President Obama's fiscal-year 2015 budget included $41 million for a Justice Department program that helps cities clear their inventories.

All that's remaining, Fairstein argued, is for authorities to get serious about the issue.

"Stories like Houston and Detroit before it are breathtaking examples of how critical it is to get this work done," she said. "The money is basically there, and certainly the government can throw more money at it. The commitment to the issue of sexual violence in all its forms is what has been such a drag on getting this done."