Barredo remained with the Joffrey School until receiving an offer to dance with the Les Grands Ballets Canadiens. In 1976, her career with Les Grands Ballets Canadiens climaxed. Renowned Cuban Prima Ballerina, Alicia Alonso, specially chose Barredo to perform on behalf of Canada at Cuba's International Ballet Festival. After this distinction, Barredo continued to dance. She danced multiple times with the famous Mikhail Baryshnikov, toured with the Stars of the World Ballet upon special invitation, and performed the role of Giselle at the Cultural Center of the Philippines Competition in 1978. After this performance, Barredo was honored with the Gawad CCP Para Sining Award of Excellence given to her by the Philippine President. Because of this, the renowned ballerina, Dame Margot Fonteyn, gave Barredo the distinction of Prima Ballerina. Barredo then continued to dance as the Philippine Ballet Theater's Prima Ballerina. After this career, Barredo returned to the United States to take the position of Prima Ballerina for the Atlanta Ballet where she would dance for twenty years before retiring. After retiring from the Atlanta Ballet, Barredo pursued a teaching career where she became the artistic consultant to Atlanta's Ballethnic and the Cultural Attache for the Philippines. In 1998, Barredo founded her own ballet school and assumed the larger role of artistic director for Metropolitan Ballet Theatre based in Atlanta, Georgia in 1998.