Lioness Asuka
González returned to Mexico and, on November 19, 1995, entered a championship tournament for the TWF Women's Championship. She defeated Bambi in the opening round, Chikako Shiratori in the semi-finals and Bison Kimura in the finals to win the title. She held the title for nearly a year until losing to Lioness Asuka in a best of three falls match at the CMLL 63rd Anniversary Show on September 20, 1996. At the CMLL 64th Anniversary Show the next year, González faced Asuka defeating her and La Diabólica in a tag team match with Lady Apache.