According to one or more aspects, the teachings herein improve user equipment (UE) Channel State Information (CSI) feedback, by letting the precoder part of a CSI feedback report comprise factorized precoder feedback. In one or more such embodiments, the factorized precoder feedback corresponds to at least two precoder matrices, including a recommended “conversion” precoder matrix and a recommended “tuning” precoder matrix. The recommended conversion precoder matrix restricts the number of channel dimensions considered by the recommended tuning precoder matrix and, in turn, the recommended tuning precoder matrix matches the recommended precoder matrix to an effective channel that is defined in part by said recommended conversion precoder matrix.