In clinical trials, adaptive allocation means that the therapies assigned to the next patient or patients depend on the results obtained thus far in the trial. Although many adaptive allocation procedures have been proposed for clinical trials, few have actually used adaptive assignment, largely because classical frequentist measures of inference are difficult or impossible to calculate when the allocation is adaptive. The general problem of making inferences in classical trials, whether randomized, adaptive, or open, is discussed; and Bayesian inference is described as being well-suited to the scientific method. Bayesian analyses of adaptive and other studies are illustrated with examples drawn from the following studies: (1) a study by R. H. Bartlett and others (1985) involving 12 patients; (2) a 39-patient study by J. H. Ware (1989); and (3) a study by D. O. Dixon and others (1989) involving 16 patients. These studies illustrate that Bayesian inference may be possible in clinical trials, but adjusting for variance is essential. Three data tables and two graphs are included. A 27-item list of references is provided. (SLD)