PATIENT CHARACTERISTICS: Age: Under 55 at time of umbilical cord blood transplantation Performance status: Zubrod 0-1 Lansky 80-100% Karnofsky 80-100% Life expectancy: At least 3 months Hematopoietic: Adequate hematologic status at time of back-up bone marrow harvest: WBC at least 3,000/mm3 Absolute neutrophil count at least 1,000/mm3 Platelet count at least 100,000/mm3 Hepatic: ALT/AST no greater than 4 times normal Bilirubin no greater than 2.0 mg/dL Renal: Creatinine no greater than 2.0 mg/dL Creatinine clearance at least 50 mL/min Cardiovascular: Normal cardiac function by echocardiogram or radionuclide scan (shortening fraction or ejection fraction at least 80% of normal value for age) Pulmonary: FVC and FEV1 at least 60% of predicted for age For adults: DLCO at least 60% of predicted Other: No active infections at time of back-up bone marrow harvest or pretransplant reduction Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception HIV negative