Somatic single-nucleotide substitutions are an important and common mechanism for altering gene function in cancer. Yet, they are difficult to identify. First, they occur at a very low frequency in the genome, ranging from 0.1 to 100 mutations per megabase, depending on tumor type1–7. Second, the alterations may be present only in a small fraction of the DNA molecules originating from the specific genomic locus for reasons including: contaminating normal cells in the analyzed sample; local copy-number variation within the cancer genome; and presence of a mutation within only a sub-population of the tumor cells8–11 (‘subclonality’). The fraction of DNA molecules harboring an alteration (‘allelic fraction’) has been reported to be as low as 0.05 for highly impure tumors8. The study of the subclonal structure of tumors is not only critical to understanding tumor evolution both in disease progression and response to treatment12, but also for developing reliable clinical diagnostic tools for personalized cancer therapy13.