Refractory AML is variously defined. MD Anderson data indicate that patients with AML that stayed in first remission for less than 2 years are incurable with standard chemotherapy regimens, hence meriting a definition of refractory; the prognosis of patients whose first remissions are longer is on average similar to that of untreated patients. Within the refractory group, Hiddeman et al' s definition (Leukemia 1990; 4: 184-188) is elaborated to account for the number of courses of initial therapy and for response to prior salvage regimens. If patients with refractory AML cannot receive an allogeneic transplant, the standard of therapy should be investigational chemotherapy regimens. A new Bayesian pre-phase II designed is described for use in testing such regimens.