Klecko moved from defensive end to defensive tackle in 1983, and was named to the Pro Bowl at his new position in 1983 and 1984. The Jets switched to a 3–4 defensive alignment in 1985, forcing Klecko to learn a new position, nose tackle. He led the Jets with 96 tackles and five forced fumbles, and tied for second with 7.5 sacks to earn his second All-Pro selection, and become the second player, after Frank Gifford, in professional football history to be selected to the Pro Bowl at three different positions. Klecko spent the 1986-87 offseason recovering from knee surgery. The knee hadn't fully healed by the start of the 1987 season, and he was limited to only seven games. After the season, the Jets released Klecko. He played one more season with the Indianapolis Colts, who went 9–7 in 1988, including a 34–16 loss to the Jets. Following the season, Klecko retired due to chronic knee problems.