Stockwell, along with teammates Greg Fasala, Neil Brooks, and Michael Delany, won another silver medal in the men's 4×100-metre freestyle relay, finishing in 3:19.68 – just 0.63 of a second behind the Americans' new world record of 3:19.05. He also teamed up with Mark Kerry (backstroke), Peter Evans (breaststroke), and Glenn Buchanan (butterfly), swimming the freestyle anchor leg to win the bronze medal in the 4×100-metre medley relay (3:43.25) behind the Americans (3:39.30) and Canadians (3:43.25). He and his freestyle relay teammates were dubbed the "Mean Machine" by the Australian media. Stockwell was the only Australian athlete to win three Olympic medals in 1984.