The purpose of the present research was to study, systematically, the "goodness-of-fit" of the one-, two-, and three-parameter logistic models. We studied, using computer-simulated test data, the effects of four variables: variation in item discrimination parameters, the average value of the pseudo-chance level parameters, test length, and the shape of the ability distribution. Artificial or simulated data representing departures of varying degrees from the assumptions of the three-parameter logistic test model were generated and the "goodness-of-fit" of the three test models to the data was studied. From the data sets analyzed in the study, it is clear that there are some sizable gains to be expected with modest length tests (n=20) in the correct ordering of examinees at the lower end of the ability continuum when three-parameter model estimates are used (as opposed to the number right score). The gains were cut roughly in half when the tests were doubled (n=40) in length. Item discrimination parameters as scoring weights had very little effect on the results. (Author)