OUTLINE: This is a randomized study. Patients receive daily hydroxyurea until their white blood cell count (WBC) is maintained at a normal level for 2-3 weeks. Patients are randomized to two groups: one group receives daily high-dose interferon alfa, and the other receives low-dose interferon alfa, 5 days per week. Both groups continue to receive hydroxyurea at reduced doses as needed to maintain a normal WBC. Treatment continues until disease progression occurs. Patients may receive cytarabine in addition to interferon in either treatment arm at the investigator's discretion. Cytarabine is given subcutaneously for 10 days every calendar month and continues in the absence of disease progression or unacceptable toxicity. Patients are followed every 6 months for survival.