IN DETROIT’S police warehouse, officials stumbled on 11,300 untested sexual-assault kits (or “rape kits”) in 2009. Each contained DNA and other evidence collected from a victim’s body just after an alleged assault; some dated back to the 1980s. “The victims never saw justice,” says Kym Worthy, a local prosecutor. In June Michigan passed a law that sets new standards for prompt testing, and there are plans to have the backlog processed by May 2015. Tests of the first 1,600 kits have already matched the DNA of hundreds of known criminals, including nearly 90 serial rapists, who have gone on to offend in 23 other states.

Tens of thousands of untested kits have been discovered in police warehouses in America, including as many as 20,000 in Texas, 4,000 in Illinois and more than 12,000 in Memphis, where three survivors are now suing the city for mishandling evidence. In addition, crime labs are estimated to have a backlog of 100,000 rape kits. Such delays betray victims. Most rapists are never caught.

Testing takes time and money. Weeks of DNA analysis can cost between $500 and $1,500 a kit, and labs are often overwhelmed. Public labs received around 4.1m requests for forensic services in 2009, which generated a queue of nearly 1.2m by the end of the year, according to the Bureau of Justice Statistics. Public labs are expanding, yet demand continues to outpace supply. Many police departments have had their budgets cut, but this is not the only problem.

Most law-enforcement bodies have discretion over what they test, and many shelve kits if a victim seems untrustworthy or a suspect has already been identified, according to the National Institute of Justice, a research arm of the Department of Justice. Police also give priority to cases in which the suspect is a stranger and the victim is visibly injured. Yet perhaps eight in ten rapes take place between people who at least vaguely know each other, and most lack signs of violence. Acquaintance rapists are often chronic offenders, says David Lisak, a clinical psychologist.

Quicker testing could prevent future attacks. In New York a programme to clear the city’s backlog has raised the arrest rate for rape from 40% to 70%. A similar crusade in Ohio has seen the state process more than half of its 8,000 kits, resulting in more than 135 indictments. A third of those charged are linked to more than one rape.

Congress has appropriated $1.5 billion to clear overdue DNA tests since 2004. Yet states are not required to spend this money on rape kits, and there is little oversight, according to the Government Accountability Office. A report by Human Rights Watch found that Los Angeles county had 12,600 untested rape kits in 2009; yet much of its federal grant money had not been used. Public attention has spurred leaders to take note. Los Angeles hired more lab analysts and ploughed through most of its arrears by 2011. Colorado, Illinois, Ohio and Texas now have laws to tackle their backlogs, and 11 more states are mulling them.