OUTLINE: This is a dose escalation study of daunorubicin in the induction therapy portion, with a separate dose escalation study of etoposide in the same portion. Patients are treated with three phases of treatment: induction, intensification, and postremission therapy. Induction therapy: Patients receive cytarabine IV as a continuous infusion on days 1-7 plus daunorubicin IV over 30 minutes and etoposide IV over 2 hours on days 1-3 (ADE regimen). Some patients also receive PSC 833 IV as a continuous infusion on days 1-3 (ADEP regimen). This course may be repeated 14 days later. Cohorts of 9 patients each receive escalating doses of daunorubicin until the maximum tolerated dose (MTD) is reached. The MTD is defined as the dose at which 3 of 9 patients experience dose limiting toxicity. Escalations are conducted separately for the ADE and ADEP regimens. Other cohorts of 9 patients each receive escalating doses of etoposide with constant doses of daunorubicin in the ADE regimen. The MTD is described in the same manner. Intensification therapy: Arm I (patients with certain genetic characteristics in their leukemia cells): Patients receive 3 additional courses of cytarabine IV over 3 hours, twice a day, for 3 days. Courses are repeated every 28 days. Arm II (patients who do not have these genetic characteristics): Patients undergo a peripheral blood stem cell (PBSC) transplant. Patients first receive high dose cytarabine IV over 2 hours on days 1-4, etoposide IV as a continuous infusion on days 1-4, and filgrastim (G-CSF) subcutaneously beginning on day 5 until blood counts recover. PBSC are then collected. Approximately 4-6 weeks later, patients receive oral busulfan 4 times a day on days 1-4 and etoposide IV over 4 hours on day 5. PBSC are reinfused on day 7. G-CSF is administered subcutaneously beginning on day 7 until blood cell counts recover. Arm III (patients who cannot undergo a PBSC transplant): Patients receive cytarabine, etoposide, and G-CSF as in arm II, then high dose cytarabine as in arm I. Postremission therapy (all patients): Patients receive low dose interleukin-2 (IL-2) by daily injection for 2 weeks. On day 15, patients begin receiving intermittent high dose IL-2 three days a week. Patients alternate these courses of IL-2: 14 days of low dose IL-2, 3 days of high dose IL-2, 1 day of rest, low dose IL-2 for 10 days, then 3 days of high dose IL-2, then 1 day of rest. This course is repeated 3 times. Patients then receive another 16 day course of low dose IL-2. Patients are followed at 1 month, then every 3 months for 2 years, then every 6 months for 2 years, then annually thereafter.