[4] On January 31, 1995, Dennis was nominated by President Bill Clinton to a seat on the United States Court of Appeals for the Fifth Circuit vacated by Charles Clark.
[7][8] Dennis's former law clerks include John Bel Edwards, the 56th governor of Louisiana,[9] and Harlin D. Hale, the former chief judge of the United States Bankruptcy Court for the Northern District of Texas.
[10][11][12] In 2014, Dennis wrote a 62-page dissent when the 5th Circuit denied an en banc rehearing for a Texas abortion law, which a 3 judge panel had upheld.
On January 18, 2019, in June Medical Services, LLC v. Gee, Dennis wrote a 19-page dissent when the 5th Circuit refused to rehear a case regarding Louisiana's abortion restrictions.
Dennis wrote: "A federal judge has already concluded that irreparable harm would flow from allowing the Executive Order to prohibit abortions during this critical time.
Moreover, I write separately to make clear that, per the Executive Order, “any procedure that, if performed in accordance with the commonly accepted standard of clinical practice, would not deplete the hospital capacity or the personal protective equipment needed to cope with the COVID-19 disaster” is exempt.
"[15] In the August 19, 2021 decision Whole Woman's Health v. Ken Paxton, Dennis dissented when a majority of the judges voted to uphold a law that bans a "dilation and evacuation", a common procedure used in second term abortions.
Dennis held: "Without such notice, Sepulvado would be subject to a death warrant and execution by lethal injection by a substance or combination of substances that might cause unnecessary pain and suffering during the execution in violation of the Eighth Amendment's Cruel and Unusual Punishments Clause—an inalterable, grievous loss entitling him, at a minimum, to notice and an opportunity to object.
'"[19] Dennis dissented when the 5th circuit, by a 10–7 vote, approved the exclusion of expert evidence in a case where a mother was sentenced to death for allegedly murdering her two-year-old daughter.
[22] On March 24, 2022, the Supreme Court reversed the Fifth Circuit and agreed with Dennis's dissent that depriving Ramirez of his spiritual advisor was unlawful.
[25] Dennis held that this section of the state constitution "requires an agency or official, before granting approval of proposed action affecting the environment, to determine that adverse environmental impacts have been minimized or avoided as much as possible consistently with the public welfare."
Dennis was one of three judges on a Fifth Circuit panel that heard the appeal to Hornbeck Offshore Services LLC v. Salazar, a case challenging the U.S. Department of the Interior six month moratorium on exploratory drilling in deep water that was adopted in the wake of the Deepwater Horizon explosion and the subsequent oil spill.
Dennis wrote a 50-page dissent, writing that "Bell’s song was not a disruption of school activities but rather was an effort to participate as a citizen in our unique constitutional democracy by raising awareness of a serious matter of public concern.
[33] In January 2020, Dennis filed a "blistering" dissent when Judge Kyle Duncan denied a transgender prisoner's appeal to update her document to include her preferred gender pronouns.
Duncan ruled against this request, writing that compelling "the use of particular pronouns at the invitation of litigants ... could raise delicate questions about judicial impartiality."
Dennis wrote that, "Ultimately, the majority creates a controversy where there is none," and that "Such an advisory opinion is inappropriate, unnecessary, and beyond the purview of federal courts."
[35] On November 23, 2020, Dennis wrote a 25-page dissent when the 5th circuit, by an 11–5 vote, permitted Texas and Louisiana to cut Medicaid funding from Planned Parenthood.
L.L.C., 140 S. Ct. at 2134 (Roberts, C.J., concurring in the judgment) (quoting 1 W. Blackstone, Commentaries on the Laws of England 69 (1765)), and to reconsider its decision to overrule circuit precedent and eviscerate Medicaid patients’ freedom of choice."
Dennis accused the majority of engaging in "a breathtaking revision of securities class action procedure that eviscerates Basic's fraud-on-the-market presumption," a reference to Basic Inc. v. Levinson in which the Supreme Court previously held that reliance may be presumed where the alleged misrepresentations were public and material, the stock traded in an efficient market, and the relevant transaction took place between the time the misrepresentations were made and the time the truth was revealed.
The Supreme Court unanimously abrogated Oscar in Erica P. John Fund, Inc. v. Halliburton Co., holding, similar to Dennis's dissent, that the Fifth Circuit's rule "contravenes Basic's fundamental premise."
[45] On July 18, 2024, Dennis dissented when the full court en banc reversed his 2023 ruling and allowed the lifetime voting ban to remain in place.