On well-constructed multiple-choice tests, the most serious threat to measurement is not variation in item discrimination, but the guessing behavior that may be adopted by some students. Ways of ameliorating the effects of guessing are discussed, especially for problems in latent trait models. A new item response model, including an item parameter to describe guessing is presented. Rather than estimating the asymptotic probability for success for a person of infinitely low ability, this parameter is shown to indicate the location on the ability scale below which guessing may be anticipated to be dominant for any item. Multiple choice item data are examined to establish typical shapes for item characteristic curves and to identify possible reasons for their unanticipated variation in the lower ability scale. The model is viewed as the sum of two logistic functions: the classical Rasch model of correct response probability, and an added function where the maximum success probability is constrained by item format (number of alternative choices) and the probability that an individual will choose to guess at random in inverse relation to the person's ability. An estimation algorithm for improved item calibration and person measurement is presented. (CM)