After completing 2 months of therapy, response to imatinib mesylate will be evaluated. If the response is good, treatment with imatinib mesylate alone will be continued. If the response is not good, the dose of imatinib mesylate will be increased to 8 tablets daily (4 in the morning and 4 in the evening) or may be decreased to 3 tablets daily. This will be based on how the drug is tolerated. Treatment may be continued for up to one year, or as long as it is judged best to control the leukemia.