|Men's canoe sprint|
|2000 Sydney||C-1 1000 m|
|2004 Athens||C-2 500 m|
|2002 Seville||C-2 200 m|
|2002 Seville||C-2 500 m|
|2002 Seville||C-2 1000 m|
|2003 Gainesville||C-2 500 m|
|Pan American Games|
|2003 Santo Domingo||C-2 500 m|
|2003 Santo Domingo||C-2 1000 m|
At the 1999 Pan American Games in Winnipeg, Balceiro duelled with Canadian Steve Giles, the reigning world C-1 1000 m champion. Giles won the C-1 1000 m final ahead of Balceiro with the positions reversed in the C-1 500 m event.
By now the Cubans were challenging the top European canoeists as well and at the Sydney Olympics, Balceiro achieved another first as he won the country's first-ever canoe/kayak Olympic medal - the C-1 1000 m silver behind Germany's Andreas Dittmer. In the C-1 500 m event, he finished sixth.
On the retirement of Leobaldo Pereira at the end of the 2001 season, Balceiro was selected as the new partner for Ibrahim Rojas in Cuba's two-man (C-2) canoe. The two men had occasionally raced together as teenagers and struck up an immediate understanding on and off the water. In 2002 they became double world champions (C-2 200 m and C-2 500 m) in Seville, Spain. They also took the silver medal in the C-2 1000 m final. The pair were voted Cuban Athletes of the Year in recognition of their achievement.
In 2003 they won both C-2 finals at the Pan American Games (500 m and 1000 m) and went to the World Championships at Gainesville, USA, as favourites. Unlike their main European rivals they again entered all three C-2 events. They finished fourth in the C-2 500 m, but were awarded bronze after the Russian team was stripped of their silver medals following Sergey Ulegin's doping disqualification. The Cuban pair had had very little recovery time since the Pan-American Games however and, this time, their grueling race schedule took its toll on Rojas and they finished outside the medals.
Both men were due to retire after the Athens Olympics and were hopeful of bowing out with a medal. Eighth place in the C-2 1000 m final was a disappointment, but the next day they won the C-2 500m silver medal.
Balceiro later decided to continue and switched back to the C-1 event for the 2005 season.
He holds the C-1 200 m world record of 38.383 seconds (Seville 2002)
- ICF medalists for Olympic and World Championships – Part 1: flatwater (now sprint): 1936–2007 at WebCite (archived 2009-01-21). Additional archives: Wayback Machine.
- ICF medalists for Olympic and World Championships – Part 2: rest of flatwater (now sprint) and remaining canoeing disciplines: 1936–2007 at WebCite (archived 2009-11-09)
- Evans, Hilary; Gjerde, Arild; Heijmans, Jeroen; Mallon, Bill. "Ledys Balceiro". Olympics at Sports-Reference.com. Sports Reference LLC.