A US appeals court has issued a temporary stay that will allow Texas to limit drop-off points to just one per county in next month's election.
Drop-off points were set up to allow voters to submit ballots in advance rather than rely on the postal service.
The decision came after another court blocked an order by Texas Governor Greg Abbott, a Republican, drastically limiting these points.
But Democrats say this amounts to voter suppression.
A record number of people are expected to vote by mail in this year's election due to the pandemic.
The US Postal Service already has already warned ballot papers may not arrive in time to be counted on election day, 3 November.
The order was first issued by Governor Abbott earlier this month. He said it would help curb "illegal voting" - mirroring President Donald Trump's claims, made without evidence, that postal voting is a major source of electoral fraud.
A federal court then blocked Mr Abbott's order in a ruling on Friday. Judge Robert Pitman told the court that it would impact vulnerable people, such as older and disabled voters.
It would force these voters to either travel long distances or to vote in person, Judge Pitman said - both of which would put them at greater risk of catching Covid-19.
However, with the latest ruling from the Court of Appeal, the state can now continue limiting the number of drop-off points.
Texas has a limit on who can request absentee ballots. Only voters who are over 65, have a disability, are in jail or who will be out of town on election day are allowed to vote by post.
Governor Abbott's ruling means that some people in Harris County, home to more than four million, will only have one point in the entire county to hand in their ballot paper.
The race to claim Texas's 38 Electoral College votes in this election is expected to be tight.
President Donald Trump has previously criticised postal voting, claiming there is widespread fraud involved. The Federal Election Commission has rejected these claims.