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In July 1986, Jolly wrote the opinion for a unanimous three-judge panel that held Louisiana's law requiring schools to teach creationism alongside evolution was an unconstitutional violation of the Establishment Clause. The decision was affirmed by the Supreme Court in Edwards v. Aguillard.
In July 2014, Jolly wrote the 2–1 majority opinion in Jackson Women's Health Organization v. Currier, which allowed Mississippi's sole abortion clinic to remain open. Jolly stated that a state law which would have shut down the clinic because its doctors were unable to obtain privileges at a local hospital would have violated Mississippi women's rights to seek abortions within their state's borders.