“These softening measures work better in theory than in practice,” said Richard L. Hasen, an election law expert and a law professor at the University of California, Irvine. “Voters don’t understand what their rights are, poll workers don’t always understand, and there’s not adequate publicity about the options.”

In Indiana, for example, an impoverished person who lacks a proper photo ID can cast a provisional ballot on Election Day, but must visit an elections office within 10 days to make the vote official and sign a statement affirming an exemption is warranted. In Texas, provisional ballots have a dismal track record, and as a result, one idea being discussed among lawyers in the case is having voters who lack the proper ID sign an affidavit and then vote on a regular ballot, not a provisional one.

Many Texas voters who cast provisional ballots because of ID-related problems — some have out-of-state driver’s licenses instead of Texas driver’s licenses — never return after Election Day with a proper ID. Their votes are never officially counted as a result. In Cameron County, where Brownsville is, 18 voters cast ID-related provisional ballots across three elections in March 2014, November 2014 and November 2015. Only one later had the vote counted, while the other 17 let their ballots expire by leaving their ID issue unresolved. In Bexar County, the location of San Antonio, 38 voters who had an ID problem cast provisional ballots in those elections. Only five returned to show the proper ID. The other 33 never followed through, and their votes did not count.

On Wednesday, the federal appeals court, the United States Court of Appeals for the Fifth Circuit, in New Orleans, ruled that the state’s voter ID law discriminated against blacks and Hispanics, in violation of the Voting Rights Act. The court ordered a federal judge in Corpus Christi — Judge Nelva Gonzales Ramos, of the United States District Court for the Southern District of Texas, who oversaw a trial in 2014 — to fashion new voter ID procedures in time for the November election.

With that vote fast approaching, the Fifth Circuit majority wrote that it would be “untenable to permit a law with a discriminatory effect to remain in operation for that election.” Complicating matters, the court did not toss out the law, which is known as Senate Bill 14 or S.B. 14. The appellate judges wrote that Judge Ramos must take into account the Texas Legislature’s desire to protect against voter fraud in fixing the problem.