Combination antimicrobial therapy has been considered a promising strategy to combat the evolution of antimicrobial resistance. Francisella tularensis is the causative agent of tularemia and in addition to being found in the nature, is recognized as a threat agent that requires vigilance. We investigated the evolutionary outcome of adapting the Live Vaccine Strain (LVS) of F. tularensis subsp. holarctica to two non-interacting drugs, ciprofloxacin and doxycycline, individually, sequentially, and in combination. Despite their individual efficacies and independence of mechanisms, evolution to the combination arose on a shorter time scale than evolution to the two drugs sequentially. We conducted a longitudinal mutational analysis of the populations evolving to the drug combination, genetically reconstructed the identified evolutionary pathway, and carried out biochemical validation. We discovered that, after the appearance of an initial weak generalist mutation (FupA/B), each successive mutation alternated between adaptation to one drug or the other. In combination, these mutations allowed the population to more efficiently ascend the fitness peak through a series of evolutionary switch-backs. Clonal interference, weak pleiotropy, and positive epistasis also contributed to combinatorial evolution. This finding suggests that the use of this non-interacting drug pair against F. tularensis may render both drugs ineffective because of mutational switch-backs that accelerate evolution of dual resistance.