California’s commission was established in 2008 by a ballot initiative. It is made up of five Democrats, five Republicans and four members not affiliated with either party. Among the commission members are a lawyer, the owner of an insurance business, an engineer, a former director of the United States Census Bureau, professors and urban planners.

In 2011, the commission redrew what Mr. Forbes called “egregious” cases of gerrymandering, including one district that had grouped Democratic voters by stretching down the Pacific Coast and then inland 100 miles to Davis, a Democratic stronghold. The redrawn legislative boundaries followed the principle that “communities of interest” should not be broken up wherever possible. In some cases that meant not mixing urban residents with rural ones or uplanders with valley dwellers; it also meant grouping residents near Long Beach worried about pollution.

Michael Li, an expert on redistricting at the Brennan Center for Justice at the New York University School of Law, said that was as it should be. “If you take a look at the legislative districts as a whole,” he said, “you should say, ‘Gosh, that looks like the state’ — not just Republicans and Democrats but the geography, the grouping of minorities. That’s what the framers wanted.”

What nonpartisan redistricting did not do, at least in California, was dent the majority party’s control of state and congressional offices. In California, where Democrats dominate, redistricting created a half-dozen newly competitive House seats, Mr. Forbes said. But Democrats actually picked up four seats and have held on to them since — a windfall that some attribute to the party’s skillful, if deceptive, gaming of the new rules.

Election law experts have been particularly critical of recent gerrymanders in Republican-controlled states like North Carolina, Wisconsin and Pennsylvania, but a lawsuit has also been filed against Maryland, where Democrats are in control.

The Constitution gives state legislatures the power to set “the times, places and manner” of federal elections, and legislators generally have been loath to cede it. A number of legislatures delegate the map drawing to commissions handpicked by the political elite, thus keeping the task political. One of them, in Pennsylvania, was accused in a state lawsuit this week of drawing one of the most gerrymandered House maps in the nation.

In states that have seriously sought to curb partisanship, it is usually voters who have pried control of political boundaries from the grip of unwilling legislators. Arizona’s bipartisan Independent Redistricting Commission sprang from a 2000 ballot initiative fiercely resisted by the state’s Republican Legislature. California voters passed Proposition 11, creating an independent commission, in 2008, four years after incumbents — mostly Democrats — swept every state legislative and congressional election. Democratic political leaders spent $7 million in a vain effort to defeat the measure.