He lost his opening match to Cuba's Alexis Rodríguez without receiving a single point on the morning session, but pulled off a 1–1 draw to tame Mongolia's Dolgorsürengiin Sumyaabazar at the end of the round-robin.

[2] When his nation Bulgaria hosted the 2001 World Wrestling Championships in Sofia, Kochev lowered his weight to less than a hundred kilograms to compete in the 97-kg division.

Despite being brought by the massive roar of the home crowd, Kochev was defeated by Russia's Giorgi Gogshelidze (who later represented Georgia in two Olympic Games) in the final match 0–3, and won a silver medal for the host nation.

[4] At the 2004 Summer Olympics in Athens, Kochev qualified for his second Bulgarian squad, as a 30-year-old, in the men's heavyweight class (96 kg) by placing third and receiving a berth from the World Championships.

[4][5] Unlike his previous Olympics, Kochev made an embarrassing exit with two straight defeats from Kyrgyzstan's Aleksey Krupnyakov (2–3) and Uzbekistan's Magomed Ibragimov (0–3), leaving him on the bottom of the pool and finishing seventeenth overall in the final standings.