Increasing resistance to antibiotics creates the need for prudent antibiotic use. When resistance to various antibiotics within a class is driven by stepwise accumulation of mutations, a dilemma may exist in regard to replacing an antibiotic that is losing effectiveness due to resistance with a new drug within the same class. Such replacement may enhance treatment success in the short term but promote the spread of highly resistant strains. We used mathematical models to quantify the tradeoff between minimizing treatment failures (by switching early) and minimizing the proliferation of the highly resistant strain (by delaying the switch). Numerical simulations were applied to investigate the cumulative prevalence of the highly resistant strain (Resistance) and the cumulative number of treatment failures (Failure) that resulted from following different antibiotic use policies. Whereas never switching to the new drug always minimizes Resistance and maximizes Failure, immediate switching usually maximizes Resistance and minimizes Failure. Thus, in most circumstances, there is a strict tradeoff in which early use of the new drug enhances treatment effectiveness while hastening the rise of high-level resistance. This tradeoff is most acute when acquired resistance is rare and the highly resistant strain is readily transmissible. However, exceptions occur when use of the new drug frequently leads to acquired resistance and when the highly resistant strain has substantial "fitness cost"; these circumstances tend to favor an immediate switch. We discuss the implications of these considerations in regard to antibiotic choices for Streptococcus pneumoniae.