Burton's all-round game made him an ideal substitute off the bench for Tall Black captain Pero Cameron when he was selected to play for New Zealand at the 2001 Goodwill Games at the age of 39. He then played a crucial part in the historic series victory over Australia later that year. Burton was still in the selection mix for the 2002 FIBA World Championship, but was replaced by Ed Book as the team's one allowable naturalised player following the team's series against Hungary.