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.