Conjoint analysts often discover that some of the part worths don't conform to expectations. We generally expect low prices to be preferred to high prices, high performance to low performance, etc. But, with individual-level CBC part worths, we often notice violations (reversals) of rational ordering. The author (Rich Johnson) investigates six alternative approaches to constraining part worths for two commercial data sets within the context of HB estimation. Two of the best methods presented in this paper are implemented in CBC/HB v1.5 software. Rich concludes: "If the primary purpose of the study is to predict individual choices, then it appears desirable to enforce monotonicity constraints. On the other hand, if the primary purpose of the study is to predict aggregate measures such as market shares, monotonicity constraints appear less helpful, and may occasionally even be harmful."