(CN) – As poll watchers for the NAACP Legal Defense Fund monitored the special election Tuesday for a U.S. Senate seat in Alabama, they found voters running into trouble casting their ballots because of a state law requiring citizens to show a photo ID to vote.

Poll workers were said to be thrown off by recently married women carrying photo IDs with names that didn’t match the names on the voter rolls, or by voters who showed up with their hair cut and dyed differently than the picture on their ID.

In Mobile, Ala., poll workers were telling voters that the address printed on their IDs had to match the address listed on the voter rolls – which is not a requirement under Alabama law, according to Deuel Ross, a civil rights attorney for the NAACP Legal Defense Fund.

On Tuesday, former U.S. Attorney Doug Jones, a Democrat, narrowly beat embattled former judge Roy Moore, a Republican accused of sexual misconduct involving teenagers 40 years ago, thanks to a notable turnout of black voters.

In a state where the names of cities such as Selma and Birmingham invoke the struggle for the right to vote, some advocates argue Alabama’s photo-ID requirement is a form of voter suppression and the special election highlighted the problem with the law.

While Jones won by about 30,000 votes, the Legal Defense Fund estimates 118,000 Alabama citizens are unable to vote because they don’t have the proper ID to do so.

“There are other close elections going on in Alabama cities and local level where the difference is 50 or 100 votes,” Ross said in an interview. “And so that’s why we think every voter [having] an opportunity to have their vote cast and have that vote be counted is important. Every time the voter ID law stops one person or 100,000 from voting, we think it’s an issue.”

Ross is one of the attorneys representing Greater Birmingham Ministries and Alabama’s NAACP chapter as they challenge Alabama’s voter ID law in a federal case that is scheduled to be heard in a Tuscaloosa courtroom in February. The Legal Defense Fund is a separate entity from the NAACP.

Jones was carried to victory by black voters who turned up on the clear December day in numbers higher than expected. According to exit polling conducted by CNN, black voters overwhelmingly supported Jones, with 98 percent of black women voting for him.

Twenty-nine percent of voters in the Alabama special election were black, according to CNN, at a time when they make up about 26 percent of Alabama’s population. While one in four people in Alabama are black, one out of every three voters in line Tuesday deciding the race between Moore and Jones was African-American.

“It could have been larger if there were people who were not facing the burden of having to obtain ID,” Ross said, adding that the voter ID requirement disproportionately affects black voters.

On Tuesday night, Jones credited minority support for his win in his victory speech.

“Y’know, I keep hearing about the different communities in this state,” he said the night of the election. “The African-American community, thank you! My friends in the Latino community, thank you! To all my Jewish friends, Happy Hanukkah!”

Moore, however, has still not conceded.

“In this race, we have not received the final count to include military and provisional ballots,” Moore said in a video shared on his Twitter account Thursday morning. “This has been a very close race and we are awaiting certification by the Secretary of State.”

The American Civil Liberties Union of Alabama also said that it saw some instances of voter intimidation and suppression on Tuesday.

“We were actually able to get some things resolved on Election Day,” ACLU of Alabama Executive Director Randall Marshall said in an interview, “but I think there is a little bit of confusion and sometimes inconsistency on the part of some poll workers about acceptable forms of ID, what you need if you’re in the inactive list and those kinds of things.”

In one instance, he said, a voter presented an acceptable form of identification but the poll worker didn’t accept it. The voter went home to get a second form of ID, which was accepted.

On Election Day, an attorney for the ACLU of Alabama called heads of law enforcement in the state capital of Montgomery because police presence at a polling location raised the question of voter intimidation.

But there are more systemic issues in Alabama, Marshall said.

“The fact that the get-out-to-vote campaign really caught fire in African-American communities is, number one, a great thing,” Marshall said, “and I think the NAACP and others did a great job of doing that, but it doesn’t undermine at all the problems that we see with the voter ID law.”

The ACLU of Alabama, Marshall said, has a long history of fighting for voting rights and launched its Know Your Rights campaign to educate voters around election season.

Marshall believes the Alabama ID law is a “piece of voter suppression” because it keeps people away from the polls who are “being discouraged to vote begin with.”

Several years ago, the state passed but did not enforce a requirement that voters had to present a photo ID to vote. As part of the 1965 Voting Rights Act, the Department of Justice reviewed any proposed change to the voting laws of Alabama and any other state or region that had a history of discriminatory rules.

This Section 5 preclearance system stopped 48 changes to Alabama’s voting laws from 1982 to 2013, until the U.S. Supreme Court said in a 2013 landmark decision that Alabama no longer need to seek preclearance. The state then announced it would start enforcing its voter ID laws requiring photo ID.

Two years later, Greater Birmingham Ministries and the Alabama NAACP challenged the law by suing state officials in Birmingham federal court, claiming they “know or have reason to know that African-American and Latino eligible voters disproportionately lack the required photo ID.”

The 2015 complaint alleged that, for example, an 18-year-old who didn’t have transportation to get to the local office for motor vehicles could not get the necessary ID to vote, and was thus harmed by the law. Around that time, Alabama also allegedly cut back its DMV locations, making it more difficult for some Alabamians to get the required identification.

Marshall said supporters of the law argue voter ID laws are needed to protect against people voting under false names or using the names of dead voters. But he says studies have shown this is rare.

“What they’re doing is using a sledgehammer to kill a fly,” Marshall said.

The office of Alabama’s secretary of state and conservative think tank Alabama Policy Institute did not respond Friday to requests for comment on the state’s voter ID law.