The three-, two- and one-parameter (Rasch) logistic item characteristic curve models are compared for use in a large multi-section college course. Only the three-parameter model produced clearly unacceptable parameter estimates for 100 item tests with examinee samples ranging from 594 to 1082. The Rasch and two-parameter models were compared for consistency and validity of item calibration and for test equating with examinee samples of 200, 600, 800 and 1082. The Rasch model provided the most consistent and valid equating. For the two-parameter model, a calibration method using average item discrimination ratios provided better results than were obtained by calibrations based on item difficulty regressions. Practical guidelines for others interested in comparing latent trait models for their own applications are provided. Although the focus of the paper is on classroom testing, the methods and recommendations are applicable to testing systems in general. (Author)