Joseph Paletta attended the US Naval Academy at Annapolis, where he tried to make the baseball team. After failing that he turned to fencing. He had some history in fencing as he had started college at New York University, where he was a fencer. In 1959 Paletta won the NCAA foil championship. His teammates, Roland Wommack and Alfonso Morales, won the épée and sabre, respectively, that year at NCAAs, the first time one school had won all three individual weapons. Paletta also fenced at the 1959 Pan American Games, winning a gold medal in team foil and a bronze in individual foil. In 1960, he was second in foil at the Amateur Fencers League of America (AFLA) tournament, which qualified him for the Olympics.