The big gun rights case the Supreme Court is set to hear on Tuesday presents the justices with a tricky problem.

They must start to clear up the confusion they created last year in a landmark decision that revolutionized Second Amendment law by saying that long-ago historical practices are all that matter in assessing challenges to gun laws. That standard has left lower courts in turmoil as they struggle to hunt down references to obscure or since-forgotten regulations.

Judging the constitutionality of gun laws has turned into a “game of historical ‘Where’s Waldo?’” Judge Holly A. Brady of the Federal District Court in Fort Wayne, Ind., wrote in December.

But this week’s case is an imperfect vehicle for achieving greater clarity about the reach of the Second Amendment.

It concerns a drug dealer from Texas with a history of armed violence who was convicted of violating a federal law aimed at preventing domestic abuse. A conservative appeals court with a reputation for extremism struck down that law, saying it had been unable to find a suitable historical analogue.

The case is, in other words, not an attractive one for groups seeking to expand Second Amendment rights. And the justices will consider it as the nation is still reeling from the deadliest mass shooting of the year, one that left 18 people dead in Lewiston, Maine.

Ever since last year’s gun rights decision, New York State Rifle & Pistol Association v. Bruen, judges have complained about the nature and volume of the work it entails, involving historical inquiries in which they have no expertise. Unable to settle on a consistent methodology, they have issued diverging decisions on not only the domestic violence law but also on ones disarming felons, 18- to 20-year-olds and users of illegal drugs.

By announcing “an inconsistent and amorphous standard, the Supreme Court has created mountains of work for district courts that must now deal with Bruen-related arguments in nearly every criminal case in which a firearm is found,” wrote Judge Brady, who was appointed by President Donald J. Trump.

The Supreme Court must use the domestic violence case to explain, refine and perhaps retreat from the new standard, said Jacob D. Charles, a law professor at Pepperdine University.

“The court has to provide further details on how to do the historical inquiry,” he said. “And that will tell us about the scope of the government’s ability to respond to gun violence that the founding generation just didn’t have to deal with.”

Writing for the six-justice majority last year in Bruen, Justice Clarence Thomas said the usual ways of assessing whether a law violates the Constitution did not apply to the Second Amendment. Only history counts, he wrote.

“The government must demonstrate that the regulation is consistent with this nation’s historical tradition of firearm regulation,” he wrote, meaning that the constitutionality of modern gun control measures depends on whether the government can show that there were analogous laws during the 18th and 19th centuries.

That test, Khiara M. Bridges, a law professor at the University of California, Berkeley, wrote last year in The Harvard Law Review, “has rendered the right to bear arms the most protected of rights in the Constitution.”

In a new study in The Duke Law Journal, Professor Charles examined more than 300 decisions applying the new standard in the 12 months after last year’s decision. More than two dozen rejected state or federal laws, including ones setting age limits, imposing strict licensing requirements, limiting so-called assault weapons and excluding guns from sensitive places.

Other studies have found that judges’ partisan affiliations are correlated to their likelihood of overturning gun regulations after Bruen.

“On average, judges appointed by Republican presidents are 1.8 times as likely to grant relief as judges appointed by Democratic presidents,” a new study to be published in the Virginia Law Review Online found. The study was conducted by Eric Ruben of Southern Methodist University, Rosanna Smart of the RAND Corporation and Ali Rowhani-Rahbar of the University of Washington.

That represents a shift, according to a preliminary analysis by Lee Epstein and Rebecca Brown of the University of Southern California and Mitu Gulati of the University of Virginia.

They found that in the 14 months before Bruen, Democratic and Republican appointees rejected Second Amendment claims at statistically the same rate. After Bruen, they found, Democratic appointees voted against the Second Amendment challenges 94 percent of the time as compared to 66 percent of the time for the Republicans ones.

“If the court in Bruen was seeking to limit judicial discretion,” Professor Epstein said, “it may have missed the mark.”

The Supreme Court’s new case started in 2019, when Zackey Rahimi assaulted his girlfriend and threatened to shoot her if she told anyone, leading her to obtain a restraining order. A judge found that Mr. Rahimi has “committed family violence” and that such violence “was likely to occur again.”

The order suspended Mr. Rahimi’s handgun license and prohibited him from possessing firearms. But Mr. Rahimi defied the order in flagrant fashion, according to court records.

He threatened a different woman with a gun, leading to charges of assault with a deadly weapon. Then, in the space of two months, he opened fire in public five times.

Upset about a social media post from someone to whom he had sold drugs, for instance, he shot an AR-15 rifle into his former client’s home. When a fast-food restaurant declined a friend’s credit card, he fired several bullets into the air.

The shootings led to a search warrant of Mr. Rahimi’s home, which uncovered weapons, and he was charged with violating a federal law that makes it a crime for people subject to domestic violence orders to possess guns.

After a judge rejected his Second Amendment challenge to the law, he pleaded guilty and was sentenced to more than six years in prison. The U.S. Court of Appeals for the Fifth Circuit at first affirmed his conviction in a short decision, rejecting the argument that the law violated the Second Amendment in a footnote.

But the appeals court reversed course after the Supreme Court decided Bruen, rejecting a variety of old laws identified by the government as possible analogues, saying they did not sufficiently resemble the one concerning domestic violence orders.

The Fifth Circuit is dominated by Republican appointees and has issued a series of aggressively conservative rulings that have met a frosty reception at the Supreme Court, itself quite conservative, on issues like immigration, abortion pills, contacts with social media companies and so-called ghost guns. Some of those Supreme Court rulings were tentative, but the overall picture is one of an appeals court out of step with the justices.

In other gun rights cases, judges have questioned the wisdom of looking to the distant past to address contemporary problems.

“An honest search for an ‘American’ tradition on gun regulation is especially challenging, given that well over half of the American population — including women, Blacks and others — were generally excluded by law from political participation at the time of the Second Amendment’s passage and for decades thereafter,” Judge Mark A. Goldsmith of the Federal District Court in Detroit, who was appointed by President Barack Obama, wrote in February.

About 30 states have laws similar to the one challenged by Mr. Rahimi.

A recent report from the RAND Corporation surveyed the available studies and found “moderate evidence” that those laws “reduce total and firearm-related intimate partner homicides.”

The federal law at issue in the case, United States v. Rahimi, No. 22-915, is not used very often, and it is seldom the sole charge when it is.

The New York Times found only 63 federal cases nationwide over the past five years of people being indicted on a charge of having a weapon while being under a domestic violence protection order, including Mr. Rahimi. Prosecutors charged a person with only the crime of possessing a gun while having a protection order in just 20 of those cases.

But the law also has a deterrent effect, both by discouraging domestic abusers subject to restraining orders from having guns and by playing a part in background checks. Since 1998, when the federal background check program started, more than 77,000 attempts by people subject to domestic violence restraining orders to buy firearms were rejected.

In defending the law, the Biden administration relied on general language in earlier decisions saying that the Second Amendment protects only “law-abiding, responsible citizens,” adding that there was nothing unusual about disarming dangerous people in the founding era.

Mr. Rahimi’s lawyers countered that the administration’s historical analogies were too expansive.

“Despite casting an incredibly broad net, the government has yet to find even a single American jurisdiction that adopted a similar ban while the founding generation walked the earth,” the brief said.

Kim Barker contributed reporting.