If questioned about their beliefs, psychometricians in one camp would argue the firm conviction that the Rasch model is mathematically elegant and intuitive as well as plausible for practitioners, pointing out the advantages of a simple model that "counts" every item in the same way. Psychometricians of another camp would argue that the three parameter logistic (3PL) model is much more flexible and is suitable to take into account that some item types have a nonzero probability to be solved by guessing and other random response strategies. Unfortunately, choosing between the 3PL and the Rasch model or other variants of item response theory (IRT) does not become easier even after it is understood that these models are closely related. If an extraneous principle such as Occam's razor is used, one may argue in favor of the simpler model; if the goal is to be more flexible in terms of the ability of the item function to fit different trace lines, a model with more parameters may seem appropriate. To make matters worse, there are alternatives that can be substituted for the 3PL model when the issue is to account for random response strategies or guessing. The author discusses these alternatives to the 3PL IRT model and introduces a more general framework useful to position the 3PL among other models for guessing.