Kinase inhibitors block proliferative signals in BCR-ABL1+ leukemic cells, but their capacity to induce apoptosis is poorly understood. Initial studies suggested that very brief exposure to kinase inhibitors was sufficient to induce apoptosis in chronic myeloid leukemia (CML) cells. However, flaws in this experimental model have subsequently been identified, leading to the conclusion that apoptosis only occurs with sustained low-level kinase inhibition. Thus, the minimum duration of complete kinase inhibition required to commit CML cells to death is unknown. Here we confirm that <1 h is insufficient to induce significant commitment to death in BCR-ABL1+ cell lines and in primary CD34+ progenitor cells, and establish that commitment to cell death only occurs if kinase inhibition is maintained for 4 h or more. Remarkably, signal transducer and activator of transcription 5 (STAT5) inhibition in combination with transient (<1 h) tyrosine kinase inhibitor (TKI) exposure proved lethal for CML progenitors, despite the reactivation of Bcr-Abl after 1 h. JAK kinase inhibition did not induce cell death in combination with transient TKI exposure. Thus, STAT5 appears to be a critical determinant of the time-dependent sensitivity of CML progenitor cells to TKI treatment in a Bcr-Abl-dependent, but JAK-independent, manner. We conclude that combining kinase inhibition with STAT5 inhibition represents a promising therapeutic approach in BCR-ABL1+ leukemias.