Cancer drivers are genomic alterations that provide cells containing them with a selective advantage over their local competitors, whereas neutral passengers do not change the somatic fitness of cells. Cancer-driving mutations are usually discriminated from passenger mutations by their higher degree of recurrence in tumor samples. However, there is increasing evidence that many additional driver mutations may exist that occur at very low frequencies among tumors. This observation has prompted alternative methods for driver detection, including finding groups of mutually exclusive mutations and incorporating prior biological knowledge about gene function or network structure. Dependencies among drivers due to epistatic interactions can also result in low mutation frequencies, but this effect has been ignored in driver detection so far. Here, we present a new computational approach for identifying genomic alterations that occur at low frequencies because they depend on other events. Unlike passengers, these constrained mutations display punctuated patterns of occurrence in time. We test this driver-passenger discrimination approach based on mutation timing in extensive simulation studies, and we apply it to cross-sectional copy number alteration (CNA) data from ovarian cancer, CNA and single-nucleotide variant (SNV) data from breast tumors and SNV data from colorectal cancer. Among the top ranked predicted drivers, we find low-frequency genes that have already been shown to be involved in carcinogenesis, as well as many new candidate drivers. The mutation timing approach is orthogonal and complementary to existing driver prediction methods. It will help identifying from cancer genome data the alterations that drive tumor progression. 