It will be a while before many others can say the same, even in Memphis. More than 12,000 kits here have been tested incompletely or not at all. Mayor A C Wharton Jr. has vowed to proceed with a $6.5 million plan to test the entire lot, appealing for state and private donations to help meet the cost and hoping that long-promised federal aid will soon appear.

The stacked-up kits are “more than pieces of evidence,” Mr. Wharton told reporters; each one represents a victim hoping for justice. He formed a task force of police officials, prosecutors and community advocates that meets twice a month to oversee the process and make monthly public reports.

Over the last decade, reports of large rape-kit backlogs have surfaced, often after investigations by news reporters or advocacy groups. But because many cities have resisted looking too hard or have even destroyed untested kits over time, the extent of the problem is unknown, said Sarah Tofte, director of policy at the Joyful Heart Foundation, a New York group that aids victims of sexual assault and is now advising Detroit and Memphis.

“What we know about the extent of backlogs around the country is still less than what we don’t know,” said Ms. Tofte, saying it appears likely that hundreds of thousands of kits still lie on shelves untested. Some of the rape kits were collected in the 1980s, before DNA analysis was fully developed, to establish blood types, something of limited use in court. But in the 1990s and after — as the technology improved and the F.B.I. set up the Combined DNA Index System, or Codis, to allow matching — a large share of kits were still not processed.

The newly concerted testing programs, when combined with the investigative heft to turn cold cases into prosecutions, are producing results.

In Detroit in 2009, officials discovered more than 11,000 unprocessed rape kits, dating back to the 1980s, in a police warehouse. Kym L. Worthy, the Wayne County prosecutor, has won praise for pursuing full testing. Analysis of the first 1,600 kits identified 455 suspects in 23 states, including 87 involved in multiple assaults, her office reported in March.