In Bangkok 2003 he easily beat Haydarov 33:13 but lost to eventual winner Gennady Golovkin 26:29 and got another Bronze.

At the PanAm Games 2003 he edged out American southpaw Andre Dirrell 21:20 but was upset in the final by Dominican Juan Ubaldo.

At the Olympics 2004 he beat Haitian-Canadian Jean Pascal and Hungarian Károly Balzsay but lost 11:12 against Andre Dirrell.

Despaigne moved up a division and reached the final of the national championships 2008 where he was upset by 18-year-old Julio Cesar La Cruz from Camagüey.

Despaigne defected to the United States along with fellow celebrated Cuban boxers Guillermo Rigondeaux and Yudel Johnson in the spring of 2009 and made his professional debut on May 22, 2009.