Abstract 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 Francisella 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 appeared to progress faster 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, under some selection conditions, the use of non-interacting drug pairs as a treatment strategy may result in a more rapid ascent to multi-drug resistance and serves as a cautionary tale. Author summary The antimicrobial resistance crisis requires the use of novel treatment strategies to prevent or delay the emergence of resistance. Combinations of drugs offer one strategy to delay resistance, but the efficacy of such drug combinations depends on the evolutionary response of the organism. Using experimental evolution, we show that under some conditions, a potential drug combination does not delay the onset of resistance in bacteria responsible for causing tularemia, Francisella. In fact, they evolve resistance to the combination faster than when the two drugs are applied sequentially. This result is surprising and concerning: using this drug combination in a hospital setting could lead to simultaneous emergence of resistance to two antibiotics. Employing whole genome sequencing, we identified the molecular mechanism leading to evolution of resistance to the combination. The mechanism is similar to the switch-back route used by hikers while scaling steep mountains i.e., instead of simultaneously acquiring mutations conferring resistance to both drugs, the bacteria acquire mutations to each drug in alternating manner. Rather than scaling the steep mountain directly, the bacteria ascend the mountain by a series of evolutionary switch-backs to gain elevation and in doing so, they get to the top more efficiently.