During therapy for chronic myeloid leukemia (CML), decline of the number of BCR-ABL transcripts has been shown to follow a biphasic pattern, with a fast phase followed by a slower phase. Hence, sustained remission requires a long phase of therapy. Data indicate that a combination of different available targeted drugs might prevent treatment failure due to drug resistance, especially at advanced stages of the disease. However, for long-term multiple-drug treatments, complications can arise from side effects. We investigate whether and how the number of drugs could be reduced during long-term therapy. Using computational models, we show that one or more drugs can be removed once the number of tumor cells is reduced significantly, without compromising the chances of sustained tumor suppression. Which drug to remove first depends on the number of mutations in the BCR-ABL gene that confer resistance to the drugs, as well as on how effectively the drugs inhibit Bcr-Abl protein tyrosine kinase activity and inhibit tumor growth. We further show that the number of CML cells at which the number of drugs can be reduced does not correlate with the two phases of decline of the BCR-ABL transcript numbers. Neither does it depend much on kinetic parameters of CML growth, except for the mutation rates at which resistance is generated. This is a significant finding because even without any information on most parameters, and using only the data on the number of cancer cells and the rate at which resistant mutants are generated, it is possible to predict at which stage of treatment the number of drugs can be reduced.