Item selection is a core component in computerized adaptive testing (CAT). Several studies have evaluated new and classical selection methods; however, the few that have applied such methods to the use of polytomous items have reported conflicting results. To clarify these discrepancies and further investigate selection method properties, six different selection methods are compared systematically. The results showed no clear benefit from more sophisticated selection criteria and showed one method previously believed to be superior--the maximum expected posterior weighted information (MEPWI)--to be mathematically equivalent to a simpler method, the maximum posterior weighted information (MPWI). (Contains 6 figures and 3 tables.)