Recent tumor sequencing data suggest an urgent need to develop a methodology to directly address intratumoral heterogeneity in the design of anticancer treatment regimens. We use RNA interference to model heterogeneous tumors, and demonstrate successful validation of computational predictions for how optimized drug combinations can yield superior effects on these tumors both in vitro and in vivo. Importantly, we discover here that for many such tumors knowledge of the predominant subpopulation is insufficient for determining the best drug combination. Surprisingly, in some cases, the optimal drug combination does not include drugs that would treat any particular subpopulation most effectively, challenging straightforward intuition. We confirm examples of such a case with survival studies in a murine preclinical lymphoma model. Altogether, our approach provides new insights about design principles for combination therapy in the context of intratumoral diversity, data that should inform the development of drug regimens superior for complex tumors. Significance: This study provides the first example of how combination drug regimens, using existing chemotherapies, can be rationally designed to maximize tumor cell death, while minimizing the outgrowth of clonal subpopulations.