Medved completed his first international jumping on January 6, 2001 at the World Cup jumping in Bischofshofen . He finished jumping on the large hill in 37th place. Two weeks later he was part of the team for the World Cup competition in Park City and surprisingly came fourth in the team competition together with Peter Žonta , Damjan Fras and Jure Radelj , ahead of the team from Germany. At the subsequent individual competition on the large hill, Medved was able to win World Cup points for the first time in 16th place. At the FIS Nordic World Ski Championships 2001 in Finland's Lahti he jumped on the normal hill at 31 and on the large hill on the 32th Place. On March 9, 2001, he jumped on the podium for the first time with third place. He was also able to convince with 6th place for ski flying at the end of the season in Planica . In the 2001 Summer Grand Prix , after two results outside the top 10, he was able to achieve 7th place in the overall ranking. On March 2, 2002, he was able to achieve 2nd place behind Finland in team jumping in the World Cup with the team together with Primož Peterka , Robert Kranjec and Peter Žonta and was on the podium for the second time in his career. In addition, the 2nd place for the Slovenian team was the best place for years. To date, no Slovenian team has been able to repeat this success. At the 2002 Ski Flying World Championships in Harrachov , which took place a week later , Medved reached 20th place. From 2002 Medved began to jump increasingly in the Continental Cup . From the 2003/04 season he jumped exclusively in the Continental Cup and was deleted from the national team. After he could not achieve any significant successes in the Continental Cup either, he ended his international jumping career in 2006.