Randomized First Choice is a new market simulation technique that shows promise for reducing IIA problems, especially when using aggregate utilities. It combines the strengths of the first choice rule and the share of preference (logit) rule. Conjoint simulators have traditionally used part worths as point estimates of preference. Most recently, Hierarchical Bayes (HB) draws and Randomized First Choice (RFC) reflect uncertainty (error distributions) about part worths. RFC makes simplifying assumptions. HB draws, though theoretically more complete, have some unexpected properties. The authors (Orme and Baker) find that RFC with point estimates performs slightly better than using HB draws during simulations. Using RFC on point estimates avoids having to use the enormous HB draws files. The authors present two reasons why HB draws did not perform as well: a reverse number of levels effect, and an excluded levels effect. This paper was delivered at the 2000 Sawtooth Software Conference.