In 1979, Nelson was initially elected to succeed the Conservative Democrat Jackson B. Davis, still a semi-retired Shreveport lawyer who did not seek another term that year. In 1988, during his last term in office, Nelson launched an unofficial candidacy for Senate president. The incumbent, Sammy Nunez of Chalmette in St. Bernard Parish east of New Orleans, had been a state representative first elected in 1964 and a senator since 1968. Nelson had traveled across the state for several years prior to 1988, having visited senators in their home districts in an attempt to secure commitments for Senate president. State Representative Ron Gomez of Lafayette, in his memoirs entitled My Name Is Ron And I'm a Recovering Legislator: Memoirs of a Louisiana State Representative, describes Nelson, accordingly: "Nelson, very professorial looking with his wire-rimmed glasses, was extremely meticulous in his approach to legislation. Although I thought his voting record was too liberal and trial lawyer-oriented, I liked the way he had conducted his campaign for Senate president. He was going after the presidency no matter who was elected governor ." Gomez said that he learned that Nelson had asked Allen Bares, a more conservative member from Lafayette, to run for president pro-tem of the Senate in conjunction with Nelson's bid for president. "That way the president would be from north Louisiana, and the pro-tem from the south. Of course, Roemer, like Nelson, was from the Shreveport area. Their meeting with Roemer was intended, of course, to get his endorsement and support ." Instead, Roemer picked Bares for Senate president and Jimmy Dimos of Ouachita Parish for House Speaker. In Louisiana, unlike most states, the governor personally selects the legislative leadership. Therefore, Nelson's "candidacy" for Senate president had always been dependent on gubernatorial preference. In 1992, Nunez returned as Senate president, as Nelson left office. Nelson was unopposed in the 1987 nonpartisan blanket primary, the last time his name appeared on the ballot. In 1990, Nelson opposed legislation authored by Senator Mike Cross to ban abortion in cases of rape and incest and impose fines of up to $100,000 and ten years imprisonment on the practitioners thereof. Governor Roemer declared the legislation incompatible with the United States Supreme Court decisionRoe v. Wade. His veto alienated large numbers of his socially conservative electoral base. The legislature subsequently overrode Roemer's veto with an even larger margin than in the original bill – another slap at Roemer. State Representative Woody Jenkins of Baton Rouge, one of the leading abortion foes in the legislature, said the prohibition regarding rape and incest is needed to prevent women from filing false claims in such matters. Nelson, however, said that he opposed the abortion ban because of the problems of unwanted children and defective births. In 1991, United States District Judge Adrian G. Duplantier of New Orleans, a former state senator, ruled that the measure was in conflict with Roe v. Wade. Nelson did not seek a fourth term in the primary election held on October 19, 1991. Instead, the Democrat Gregory J. Barro of Shreveport led the field with 11,224 votes. Republican Ronald Bradford "Ron" Fayard, a Realtor, Mississippi native, and civic leader from Bossier City, trailed with 10,228 votes. The Democrat and later a Republican judge, Parker Self of Bossier City received 29 percent of the vote; a second Republican candidate, Shreveport attorney Leroy Havard Scott Jr., held the remaining 5.5 percent of the ballots cast. In the general election, Barro defeated Fayard, 22,616 to 15,803.
