Deák-Bárdos had also won a total of five silver medals at the World Championships, losing out to numerous top-level wrestlers including Alexander Karelin, Rulon Gardner, Khasan Baroyev, and Mijaín López, all of whom were Olympic champions in the same division.

After Karelin's retirement in 2000, Deák-Bárdos continued to build success in wrestling by capturing four medals for the super heavyweight division (120–130 kg) at the European Championships, including his first-ever gold from Moscow.

He managed to repeat his silver medal streak at the World Championships, when he lost the final match to United States' Rulon Gardner (2001) and Dremiel Byers (2002), and to Russia's Khasan Baroyev (2003), who succeeded Karelin to become an Olympic champion in 2004.

He placed second in the preliminary pool against Bulgarian wrestler and 1996 Olympic bronze medalist Sergei Mureiko and Russia's Alexander Karelin, who previously defeated him at the World Championships three years before, finishing overall in 11th position.

Once again, he repeated his position in the preliminary pool this time, against Finland's four-time Olympian Juha Ahokas and Iran's Sajjad Barzi, who eventually lost to defending Olympic champion Rulon Gardner in the bronze medal bout.