Since its release in 1976, LOGIST has been the most widely used computer program for estimating the parameters of the three-parameter logistic item response model developed by A. Birnbaum. An alternative program, BILOG, developed by R. J. Mislevy and R. D. Bock (1983), has recently become available. This paper compares the approaches taken by the two programs and offers some initial guidelines for choosing between the two programs for particular applications. An application of the two programs to two simple simulated data sets is illustrated, wherein responses are assessed from simulated examinees to a 45-item artificial test comprised of three replications of 15 four-choice items. It is recommended that: (1) the user with short tests and/or small examinee samples consider using BILOG due to its incorporation of formal Bayesian procedures, while LOGIST performs better with longer tests and larger samples; (2) LOGIST can produce joint maximum likelihood estimates, while BILOG can produce marginal maximum likelihood estimates; and (3) neither program alone can produce finite and reasonable parameter estimates. A list of references, three data tables, and 19 graphs are provided. (TJH)