 In 1963, Besa won the unofficial cup competition held by the 'Sport' newspaper, and in 1965 it won the 'Bashkimi' newspaper competition.The period between 1965 and 1975 has been called the golden generation of football in Kavajë, due to the domestic achievements especially in the Albanian Cup which resulted in the club's first ever European games.In 1971, they finished as runners-up in the Albanian Cup after losing 2–0 in the finals to Dinamo Tirana.