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After beating title contender Arturo Morua, he would then lose a very disputed decision to IBO Light Welterweight World Champion Colin Lynes.
He mainly fought in Mexico for first three years, then moved the main battlefield to the United States since 1983, and won the World Boxing Council (WBC) junior welterweight title by beating Lonnie Smith via the fifth round on a technical knockout (TKO) in 1986.
Alexander climbed into the welterweight division after struggling to make weight against Andriy Kotelnik, WBO junior welterweight beltholder Timothy Bradley and Lucas Matthysse.
He was to fight WBA champion Aaron Pryor in the summer of 1982 for a unification bout in the junior welterweight division, but instead fought and lost (both match and title) by split-decision to Leroy Haley in June of that year.
In February, Matthysse scored his most notable win, a controversial fourth-round stoppage of former junior welterweight Vivian Harris.