Aycock presumably could have had a fourth term as lieutenant governor for the asking, but he entered the 1971 Democratic primary for governor. The field was so crowded that the lieutenant governor never made it into the top tier of candidates, headed by then U.S. Representative Edwin Washington Edwards of Crowley, State Senator J. Bennett Johnston, Jr., of Shreveport, then former U.S. Representative Gillis William Long of Alexandria, and former Governor Jimmie Davis, then of Baton Rouge. Aycock, the most conservative candidate in the field, finished in sixth place with 88,465 votes. Davis and Aycock, who had been the winning intraparty ticket in 1960, were opposing each other in 1971. As it turned out, neither was a serious factor in the race.