This is a Phase II study of perifosine in patients with refractory and relapsed leukemia. After a one time loading dose of 600 mg (150 mg x 4 at least 4 hours apart) during the first cycle, perifosine will be given orally at 100 mg once a day continuously. Cycles are 28 days in length. Intra-patient dose escalation for the maintenance dose to 150 mg daily will be done in the second cycle if no non-hematological toxicities beyond grade 0-1 occurred during the first cycle are observed.