[1] Jones was nominated by President Ronald Reagan on February 27, 1985, to the United States Court of Appeals for the Fifth Circuit, to a new seat authorized by 98 Stat.

In 2010, Jones visited Iraq as part of the U.S. State Department's Rule of Law program, where she advised and encouraged Iraqi and Kurdish judges.

[6] The Chicago Sun-Times and several other newspapers reported on July 1, 2005, that she had also been considered for nomination to the Supreme Court during the presidency of George W. Bush.

[8][9] In May 2018, Jones wrote for the court when it found that Texas Senate Bill 4, which prohibits local governments or public employees from "endorsing" sanctuary city policies, did not violate the First Amendment.

Jones joined the Fifth Circuit in rejecting the petition on procedural grounds, but she took the unusual step of handing down a six-page concurrence to the judgment of the court.

The concurrence credited the evidence presented by McCorvey and sharply criticized the Supreme Court's rulings in Roe and in a less famous case that was decided simultaneously, Doe v. Bolton.

She quoted Justice Byron White's dissent in the latter that described the Supreme Court's decision as an "exercise of raw judicial power".

[12] She concluded: "That the court's constitutional decision making leaves our nation in a position of willful blindness to evolving knowledge should trouble any dispassionate observer not only about the abortion decisions, but about a number of other areas in which the court unhesitatingly steps into the realm of social policy under the guise of constitutional adjudication.

[20] On August 12, 2014, the judicial ethics panel of the District of Columbia Circuit dismissed the complaint by citing lack of evidence to justify disciplining Jones.