From 1962 Brandtzæg was part of the Norwegian national team. His first international tournament was the Four Hills Tournament 1962/63 , in which he reached 5th place in the overall tournament ranking. In 1963 he won the Norwegian Ski Jumping Championships for the first time in Kristiansand in front of Torbjørn Yggeseth and Arnfinn Malm . In 1964 he repeated this success in Voss before Toralf Engan and Hans Olav Sørensen . He was then part of the squad for the 1964 Winter Olympics in Innsbruck . There he won bronze medals on both the normal and the large hill.
At the Four Hills Tournament in 1964/65 , after two day victories in Oberstdorf and Innsbruck , he was able to achieve first place in the overall standings and thus celebrated the greatest success of his career. In the same year he won again the silver medal on the normal and the gold medal on the large hill at the Norwegian Championships in Bærum . Because of a complicated broken leg that he suffered at the end of the 1964/65 season, he confirmed on February 16, 1966 that he would no longer be able to participate in any sport.