After the 1998 season and a successful 1998 European Handball Championship in Italy, Savukynas transferred to UMFA Afturelding in Iceland. While playing for UMFA Afturelding in 1999, he won every possible title in Iceland – Champions Cup, Iceland Handball Cup, Iceland Handball League (for the first and only time in the club history) . In 2000, Savukynas was named as the best offensive player of Iceland Handball league. In 2001, Savukynas moved to play in Switzerland for the top division team TV Zofingen. During that period, Savukynas was one of the top scorers in the league.
