As the rates of most cancers are proportional to the fourth to fifth power of age ("log-log" behavior), it is widely believed that 5 to 6 independent mutations are necessary for malignant transformation. Conversely, the peak incidences of most cancers are similar to stem-cell mutation rates at single loci, implying only one rate-limiting mutation. Here, flow cytometrically measured red blood cells mutated at a selectively neutral locus, glycophorin A, allow observation of individual stem-cell differentiation events in a log-log malignancy, polycythemia rubra vera. Contrary to predictions from multistep models, the clone is driven by infrequent (< annual) and rare ( approximately 18 per year) differentiation events. These parameters imply that malignant stem cells have a modest selective advantage. Correspondingly minor, typically less than 20%, increases in stochastic self-renewal ratios are modeled to show that single mutations can result in the observed fourth power relationship with age. The conundrum between log-log behavior and mutation rate is thereby reconcilable, with the age of onset arising not from the requirement for multiple, independent mutations but from infrequent, stochastic stem-cell division rates and single mutations causing initially minor effects, but initiating a clone whose expected number increases successively with age--an "exponential phenotype."