Last fall, Deputy Vrotsos told about 30 of the offenders that they would have to move to meet the requirements of Iowa's law, which he said made about 90 percent of the city of Dubuque off limits.

Some complied, he said, moving to trailer parks, across the Mississippi River into Illinois, to motels or, in the case of one man who had been living with his parents, to a truck at the Ioco Truck Stop on the outskirts of town. But at least three of the offenders have disappeared, Deputy Vrotsos said, giving false addresses or not providing any address at all.

The effectiveness and fairness of the restrictions has become a matter of great debate.

Some law enforcement officials say they believe that restrictions keep the most serious sexual predators away from places where they would be most likely to hurt a child again. But others argue that while such laws are politically appealing, there is little empirical evidence to suggest a connection between recidivism and proximity to schools or day care centers, and that the policies are too broad, drawing in, for example, people who as teenagers had sex with an under-age girlfriend.

In Arkansas, a 2001 study found that sexual offenders of children often lived near schools, day care centers and parks. Those results suggested, said Jeffrey T. Walker, a professor from the University of Arkansas at Little Rock who was a co-author of the research, that residency restrictions could be a reasonable deterrent.

But studies for the Colorado Department of Public Safety in 2004 and the Minnesota Department of Corrections in 2003 have suggested that where an offender lives appears to have no bearing on whether he commits another sex crime on a child.

The problems have left some states turning to other means for controlling registered sex offenders, particularly with public outcry after cases like the rape and killing of 9-year-old Jessica Lunsford in Florida last year; a convicted sex offender is accused in the attack.

A flurry of new legislation is being considered all over the country. More legislatures are considering joining a dozen that already use satellite tracking devices on offenders. Others, including Iowa, are considering harsher prison sentences for those who attack children. Lawmakers reason that they would not have to worry about recidivism if offenders rarely emerged from prison.