Alternating antibiotic therapy, in which pairs of drugs are cycled during treatment, has been suggested as a means to inhibit the evolution of de novo resistance while avoiding the toxicity associated with more traditional combination therapy. However, it remains unclear under which conditions and by what means such alternating treatments impede the evolution of resistance. Here, we tracked multistep evolution of resistance in replicate populations of Staphylococcus aureus during 22 d of continuously increasing single-, mixed-, and alternating-drug treatment. In all three tested drug pairs, the alternating treatment reduced the overall rate of resistance by slowing the acquisition of resistance to one of the two component drugs, sometimes as effectively as mixed treatment. This slower rate of evolution is reflected in the genome-wide mutational profiles; under alternating treatments, bacteria acquire mutations in different genes than under corresponding single-drug treatments. To test whether this observed constraint on adaptive paths reflects trade-offs in which resistance to one drug is accompanied by sensitivity to a second drug, we profiled many single-step mutants for cross-resistance. Indeed, the average cross-resistance of single-step mutants can help predict whether or not evolution was slower in alternating drugs. Together, these results show that despite the complex evolutionary landscape of multidrug resistance, alternating-drug therapy can slow evolution by constraining the mutational paths toward resistance.