Benavides was nominated by President Bill Clinton on January 27, 1994, to a seat on the United States Court of Appeals for the Fifth Circuit vacated by Judge Thomas Gibbs Gee.

Burdine, who had received a death sentence for capital murder in Texas, had petitioned the federal courts for a Writ of habeas corpus.

After hearing the case, Judges Rhesa Barksdale and Edith Jones ruled for the court that Burdine's claim did not, in and of itself, warrant issuance of the writ and grant of a new trial.

The United States Supreme Court took up the case, and in a sharply-worded opinion (Tennard II), held that the Fifth Circuit law Benavides had used was wrong.

Justice Sandra Day O'Connor wrote that Benavides' opinion had merely paid "lipservice" to important principles and had used a test that "has no foundation in the decisions of this Court.

After Congressman Tom DeLay resigned from Congress, the Republican Party of Texas sought to replace him with another candidate on the ballot shortly before the 2006 election.

In court, the Republican Party argued that Tom DeLay was in fact ineligible to run for Congress in Texas because he had recently moved to Virginia.

Benavides, writing for a unanimous three-judge panel of the Fifth Circuit that included conservative Republican appointee Edith Brown Clement, ruled in favor of the Democrats.

According to Benavides, the plain language of the Constitution says that candidates for Congress only need be residents of the requisite state, in this case Texas, as of election day.

"[13] The Houston Chronicle wrote, "The laudable impartiality by the judges making these politically sensitive rulings should strengthen the confidence of all parties that they can get a fair day in federal court.