Savon did fight in the 1992 Games. In the quarterfinals, he faced an unexpected obstacle: Danell Nicholson of the United States. Savon was forced to come from behind in the last round to win 13-11. The rest of his bouts were easy, and culminated in a 14-1 victory in the final over David Izonritel of Nigeria.
Savon was not seriously challenged at the 1996 Olympic Games, winning a second gold medal by beating David Defiagbon of Canada 20-2. At the Sydney Games of 2000, Savon, by now 33 years old, again won easily, defeating Sebastian Köber of Germany 14-8 in the semifinals and Sultan Ahmed Ibragimov of Russia 21-13 in the final. Savon, who stood 1.98m, is one of only three boxers to win three gold medals.