Deregulated BCR-ABL oncogenic activity leads to transformation, oncogene addiction and drives disease progression in chronic myeloid leukemia (CML). Inhibition of BCR-ABL using Abl-specific kinase inhibitors (TKI) such as imatinib induces remarkable clinical responses. However, approximately only less than 15 % of all chronic-phase CML patients will remain relapse-free after discontinuation of imatinib in deep molecular remission. It is not well understood why persisting CML cells survive under TKI therapy without developing clonal evolution and frank TKI resistance. BCR-ABL expression level may be critically involved. Whereas higher BCR-ABL expression has been described as a pre-requisite for malignant CML stem cell transformation and CML progression to blast crisis, recent evidence suggests that during persistence TKI select for CML precursors with low BCR-ABL expression. Genetic, translational and clinical evidence is discussed to suggest that TKI-induced maintenance of low BCR-ABL signaling output may be potently tumor suppressive, because it abrogates oncogenic addiction.