Some patients with Philadelphia (Ph) chromosome-positive chronic myeloid leukemia (CML) may achieve partially or completely Ph-negative hemopoiesis after treatment with high doses of cytotoxic drugs or interferon-alpha at standard dosage. This observation leads to three important questions: 1) are Ph-negative myeloid cells in such patients strictly normal? 2) can such Ph-negative cells be identified in all newly diagnosed patients or only in a minority? and 3) what is the basis for the proliferative advantage manifested by CML cells and why might it be temporarily lost as a result of treatment? The mechanisms that might prevent the proliferation of normal cells in an environment of Ph-positive cells and the relevance of these questions to the design of a strategy aimed at obtaining complete remission in the majority of patients are considered. Such a strategy might incorporate autografting with Ph-negative stem cells harvested during the recovery phase of high dose chemotherapy.