One approach to testing the goodness of fit of a completely specified continuous distribution when only a subset of the ordered sample is available is to transform that subset into a complete uniform ordered sample of smaller size. After this, any of the classical tests for uniformity may be used. Two systematic procedures for transforming a subset of the ordered sample are studied, and they are illustrated when the subset results from single censoring of the data on the left or right or at both extremes. The procedures are derived from Rosenblatt's transformation and are shown to coincide for Type II singly censored data at one extreme with a procedure proposed earlier by Michael and Schucany (1979). A Monte Carlo power study was conducted to analyze the relative merits of the procedures followed by the Anderson-Darling AZ test for uniformity for some types of censoring.