In 1965, Brady joined the staff in
Washington, D.C., of
U.S. Representative Speedy O. Long of
Louisiana's 8th congressional district, since disbanded. He worked for Long until 1971; after a failed gubernatorial campaign, Long left Congress in 1973 and became the LaSalle Parish
district attorney. At the age of thirty-seven, Brady was elected in 1975 to the Louisiana House in the first ever
nonpartisan blanket primary system held in Louisiana. From 1984 to 1987, he was the vice chair of the House Administration of Criminal Justice. He was also a member of the House Education Committee. Brady prevailed by 207 votes in the
runoff election, 7,301 (50.7 percent) to 7,094 (49.3 percent) for Rambo. Without his strong support in La Salle Parish, Brady would have been defeated. In 1986, Brady challenged the incumbent, fellow Democrat
Jerry Huckaby of
Bienville Parish, for
Louisiana's 5th congressional district seat, which Huckaby had held for a decade. Huckaby prevailed with 96,200 votes (68.5 percent) to Brady's 32,284 ballots (23 percent), and 11,966 votes (8.5 percent) for the
Monroe businessman Fred W. Huenefeld. Brady won only in La Salle Parish and only by 154 votes. In 1987, in his bid for a fourth term in reconfigured House District 22 (Grant, La Salle, and Rapides parishes), Brady led in the primary against six other Democrats but was forced into a
runoff election against A. Dale Smith, who trailed by about 1,500 votes. Smith prevailed in the second balloting, 8,111 (54.1 percent) to 6,893 (45.9 percent). Brady won only narrowly in his own LaSalle Parish and lost Grant and Rapides parishes. ==Personal life==