Randomized studies involving long-term follow-up are vulnerable to the effects of unplanned crossover. In surgical studies, such crossover usually occurs when control patients become more symptomatic and undergo operation. In several large studies of coronary bypass grafting, crossover ranged from 25% to 38%. The most common way of dealing with this problem is to apply the "intention-to-treat" principle, which analyzes such crossovers with their originally assigned groups. Besides the logical problem of counting a control patient who actually undergoes operation as "nonsurgical," a more subtle problem arises in terms of statistical power. When statistical power is low, a truly effective treatment may be mistakenly labeled as no better than control, causing a potentially valuable form of therapy to be ignored or discarded. This analysis demonstrates that crossover may have a profound effect on the statistical power of randomized studies and presents a method for predicting the effect of such crossover on statistical power.