 Patients receive alvocidib intravenously IV over 412 hours once weekly in weeks 1-4. Treatment repeats every 6 weeks for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients achieving stable disease after 4 courses of therapy discontinue study treatment. Patients who achieve complete remission CR receive 1 additional course of therapy beyond documentation of CR. Cohorts of 3-6 patients receive escalating doses of alvocidib until the maximum tolerated dose MTD is determined. The MTD is defined as the dose preceding that at which 2 of 3 or 2 of 6 patients experience dose-limiting toxicity. A total of 10 patients are treated at the MTD. 