Voter fraud is rare in the U.S.—so rare that its use as a rationale for strenuous campaigns to tighten voting requirements is highly suspect. Nevertheless, since the last general election, Republicans have been busy around the country putting rules in place to make it more difficult to vote, and to register people to vote.

That movement, however, was brought sharply to heel last week by court decisions in Ohio, Texas and Florida.

*Two decisions affecting Ohio will make voting easier there. One is an injunction against a law dating from 2006 that requires ballots cast at the wrong polling place to be thrown out even when voters went to those places at the direction of poll workers. Another decision expected to affect a larger number of voters is one that restores weekend voting in Ohio, a practice that was instituted for the 2008 election to avoid the long lines that had caused some voters to give up and leave the polls without voting in 2004, but prohibited by a 2011 Republican initiative.

*In Florida, the issue was voter registration. Last year Republicans in the state government, including conservative Gov. Rick Scott, put through a law that required such third parties as the League of Women Voters and Rock the Vote to hand in the completed registration forms harvested during registration drives within 48 hours or pay a prohibitive penalty of $50 per form. Some organizations simply shut down their drives rather than risk paying the fines. But last week Judge Robert Hinkle overturned the new rules in U.S. District Court in Tallahassee.

*A voter identification law passed in Texas was overturned by a federal appeals court in the District of Columbia on the grounds that it was discriminatory. Because “a disproportionately high percentage of African Americans and Hispanics in Texas live in poverty,” the court said, the law would create an obstacle for members of those groups and could not be allowed to stand.

A recent study by News21, a national investigative reporting project funded by the Carnegie Corporation of New York and the John S. and James L. Knight Foundation, with National Public Radio, NBC.com, the Washington Post and other major media as partners, looked at the incidence of voter fraud in the U.S. The researchers found that in 10 years of elections, with 146 million Americans voting, there were 2,068 allegations of voting irregularity, including invalid registration, misuse of absentee ballots, impersonation, double voting and more; of the cases whose outcome could be determined, 46 percent resulted in acquittals, dropping of charges or refusal to bring charges. In all those years there were only 10 cases of impersonation, the kind of voter fraud that could be prevented by voter ID requirements.

So if voter fraud is not common enough to threaten the integrity of elections here, why is someone acting as if it is a threat? Consider these statistics from Florida, where the effort to register new voters—which often means poor and minority voters—has been chilled for a year. Normally for the 13 months leading up to the first of July before a November election, the number of registered Democratic voters in that state rises by over 200,000. But for the 13 months before this past July 1, that number increased by only 11,365. The number of registered Republicans in Florida, however, rose by 128,039.