Brief Summary: This randomized phase II trial studies how well giving rasburicase together with allopurinol works in treating patients with hematologic malignancies. Rasburicase may reduce the level of uric acid in the blood. Allopurinol may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. It is not yet known which dose of rasburicase is more effective in treating hematologic malignancies when given together with or without allopurinol.

Detailed Description: PRIMARY OBJECTIVES: I. To prospectively evaluate the efficacy, as defined by uric acid response rate, of 2 different single low doses of rasburicase followed by allopurinol in 2 treatment arms. SECONDARY OBJECTIVES: I. To estimate the proportion of patients requiring additional doses of rasburicase to maintain a uric acid level =\< 7.5mg/dL on day 2 through day 6. II. To identify differential characteristics of the patients who do not respond to treatment. III. To measure the area under the plasma uric acid concentration-time curve (AUC) from baseline (day 1) to day 7, time to plasma uric acid level less than or equal to 7.5mg/dL. IV. To evaluate the rate of patients requiring hemodialysis (HD) V. To evaluate the safety of low single-doses of rasburicase. VI. To evaluate the rate of patients expressing a doubling of serum creatinine. OUTLINE: Patients are randomized to 1 of 2 treatment arms. ARM I: Patients receive 1.5mg of rasburicase intravenously (IV) over 30 minutes on day 1\* and allopurinol orally (PO) once daily (QD) on days 1-6. ARM II: Patients receive 3 mg of rasburicase IV over 30 minutes on day 1\* and allopurinol PO QD on days 1-6. NOTE: \*Patients with serum uric acid \>= 7.5mg/dl also receive rasburicase IV on days 2-3. After completion of study treatment, patients are followed up at 30 days.