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Democrats in Virginia claimed a victory on parts of a voting rights lawsuit in the state, with a settlement on the portion related to long waiting times for voters to cast ballots, especially in precincts with large numbers of minorities residents.

The settlement, hammered out in a consent decree by the United States District Court in the Eastern District of Virginia in the case, rules that there will be major changes by the state Board of Elections and Department of Elections to lay out guidelines about how to handle paper ballots in the case of machine breakdowns, and finding solutions to help local boards with the issue of long lines. In some cases, there have been reports of voters waiting hours before casting their ballots.

The settlement on the long-lines part of the larger suit came less than a year before the presidential election. Virginia is a crucial battleground state, with an electoral composition that is reflective of demographic changes in the rest of the country.

“This settlement is a tremendous step forward for Virginia voters and for the commonwealth’s efforts to make democracy as accessible as possible to the people we serve,” Gov. Terry McAuliffe said in a statement. Mr. McAuliffe is a close ally of Hillary Clinton, who leads in most polls for the Democratic presidential nomination.

Mr. McAuliffe added, “I look forward to working with the Virginia Department of Elections to implement these reforms so that no voter is forced to wait hours in order to have a say in the future of our commonwealth and country.”

The remaining parts of the suit relate to trying to strike down the state’s voter-identification law, which still faces a trial in January.

Mrs. Clinton has made voting rights an important aspect of her candidacy. Democrats have for the last three years been focused on changes in states around the country where, they argue, new laws are onerous and make it harder for poorer citizens, many of whom are black and Hispanic, to vote.