in the NAIA District Playoffs. They were beaten in two games by Texas State, 83–64 and 73–72. In 1962, the Broncs finished with a 26–4 record. This time, the Broncs finally made their first NAIA Men's Basketball Tournament appearance after beating Texas State twice in a row, 71–68 and 67–61. The Broncs got to the second round before losing to the Ferris Institute. This was their final season in the Big State Conference, with the Broncs becoming an Independent after the season ended. The Broncs finished 25–6 in the 1962–63 season. They beat McMurry 77–51 in the NAIA District Playoffs to make their second straight NAIA National Tournament appearance. The Broncs subsequently won the 1963 NAIA Division I men's basketball tournament, winning five games by an average margin of 20.4 points. Lucious Jackson was awarded the Chuck Taylor Most Valuable Player Award for his 93 rebounds in 5 games for an average of 18.6 rebounds per game. The following year, the Broncs finished with a 28–6 record, the most victories the team ever had in a season. Once again, the Broncs prevailed in the NAIA District Playoffs, beating McMurray 86–81 to advance to the Tournament again. The Broncs went to the NAIA national championship once again, but they lost to Rockhurst. Despite the loss, Lucious Jackson was awarded the Chuck Taylor Most Valuable Player Award once again, for his 67 rebounds in 5 games (for a 13.4 rebounds per game average) and his 124 total points for a 24.8 game average. In his three tournaments, he scored a total of 301 points and 180 rebounds. In 1965, the Broncs finished 19–7, but they failed to advance past the NAIA District Playoffs in three games, including the final game by one point in Edinburg. The following year, they finished 15–12, but lost in the NAIA District Playoffs again, this time to Midwestern State, 81–77 and 84–75. A 15–9 season the following year failed to yield another shot at the District Playoffs. In 1968, the Broncs (which had become Pan American University in 1965) qualified for the 1968 NCAA College Division men's basketball tournament with a 21–6 record culminated by a 19–3 end to a season that had zero losses at home. They were placed in the Southwestern Region. They beat Jackson State 96–73 to reach the regional final and potentially be one of the last 16 teams in the national finals.