The independent block structure of regenerative processes and the known convergence rates of the means of ratio estimators are exploited to produce biasreduced regression-adjusted estimates (rare's) for regenerative simulations. Formal and graphical assessments of the evolution of the distributions of the estimates to normafity and symmetry are given. Other graphs show the evolution of the bias in the estimates as well as the bias reduction achieved by the rare estimate. A protocol for guiding the analyst in the interactive and sequential use of the methodology is described. Sample graphs for the output of congested M/G/1 queueing simulations are displayed illustrating the application of the protocol. Empirical sampling tests on the statistical properties of the rare's are also reported. © 1981, ACM. All rights reserved.