Patients receive induction therapy comprising clofarabine IV on days 1-5 and gemtuzumab ozogamicin IV over 2 hours on days 1, 4, and 7 during course 1 only. Beginning in course 2, after blood counts recover, patients receive consolidation therapy comprising clofarabine IV on days 1-5. Consolidation treatment repeats upon blood count recovery for up to 2 courses in the absence of disease progression or unacceptable toxicity.