Antibiotics have greatly reduced the morbidity and mortality due to infectious diseases. Although antibiotic resistance is not a new problem, its breadth now constitutes a significant threat to human health. One strategy to help combat resistance is to find novel ways to use existing drugs, even those that display high rates of resistance. For the pathogens Escherichia coli and Pseudomonas aeruginosa, pairs of antibiotics have been identified for which evolution of resistance to drug A increases sensitivity to drug B and visa versa. These research groups have proposed cycling such pairs to treat infections, similar treatment strategies are being investigated for various cancer forms as well.While an exciting treatment prospect, no cycling experiments have yet been performed with consideration of pharmacokinetics (PK) and pharmacodynamics (PD). To test the plausibility of this scheme and search for ways to optimize it, we create a mathematical model with explicit PK-PD considerations. We study several possible treatment protocols using pairs of such antibiotics, and investigate the speed of ascent of multiply resistant mutants. Our analyses show that for low concentrations of antibiotics, treatment failure will always occur due to the rapid ascent and fixation of resistant mutants. However, at moderate to high concentrations of some types of bacteriostatic antibiotics with multiday cycling, resistance is prevented from developing and treatment succeeds. This calls for guarded optimism of such treatment protocols whose development can be directed by these types of models.