Cohorts of 3-6 patients receive escalating doses of homoharringtonine until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose at which 2 of 6 patients experience dose-limiting toxicity. An additional cohort of 25-30 patients with chronic phase chronic myelogenous leukemia receives remission induction and maintenance therapy as above at the MTD. (Phase I completed as of 2/11/2004.)