A federal judge who is expected to rule soon in a lawsuit over whether same-sex couples should be allowed to marry in Louisiana has denied a request from one of the couples involved to present additional oral arguments.

That means, for the most part, that all either side of the case can do now is wait for a ruling.

In a one-paragraph order Monday, U.S. District Judge Martin Feldman said he has studied the latest filings from each side and found “no further briefing or argument is necessary.”

Feldman heard arguments in federal court in New Orleans last month on the question of whether Louisiana should have to recognize same-sex marriages performed legally in states that already allow them.

He asked for additional briefs on whether gay or lesbian couples also should be allowed to obtain marriage licences in Louisiana, as well as whether state officials are violating the First Amendment rights of married same-sex couples by forcing them to list themselves as single on state tax forms. Those briefs arrived last week.

One of the couples involved, Robert Welles and Garth Beauregard, asked for a chance to make additional oral arguments to bolster their case for obtaining a marriage license here, but Feldman has ruled that out.

Whichever way the judge decides, the case is most likely headed next to the 5th U.S. Circuit Court of Appeals, which hears cases from Louisiana, Texas and Mississippi.

Many advocates on both sides of the issue expect the U.S. Supreme Court to eventually take up the main question involved: whether state bans on same-sex marriage violate the U.S. Constitution.