The recently developed case-cohort method of sampling from a cohort is compared with the nested case-control method. Corrected asymptotic relative efficiency results show that the case-cohort design for single "disease" outcomes offers less improvement for intervention trials for which there is no random censoring than originally suggested. Furthermore, simulation results indicate that if there is moderate random censoring or staggered entry, the case-cohort method can do substantially worse than the nested case-control method.