Chronic myeloid leukemia (CML) is a cancer of the hematopoietic system and has been treated with the drug Imatinib relatively successfully. Drug resistance, acquired by mutations, is an obstacle to success. Two additional drugs are now considered and could be combined with Imatinib to prevent resistance, Dasatinib and Nilotinib. While most mutations conferring resistance to one drug do not confer resistance to the other drugs, there is one mutation (T315I) that induces resistance against all three drugs. Using computational methods, the combination of two drugs is found to increase the probability of treatment success despite this cross-resistance. Combining more than two drugs, however, does not provide further advantages. We also explore possible combination therapies using drugs currently under development. We conclude that among the targeted drugs currently available for the treatment of CML, only the two most effective ones should be used in combination for the prevention of drug resistance.