Example embodiments are presented for codebook subset restriction and precoder selection in wireless communications systems. For instance, an example method for codebook subset restriction at a user equipment (UE) is presented. In the example method, the UE can receive, from a network node such as a gNB, codebook subset restriction (CBSR) signaling for a first component common to precoders in a first group of codebooks. In an aspect of the present disclosure, a restriction of the first component maps to a restriction of a second component and the second component is common to precoders in a second group of codebooks. In addition, the example method includes restricting precoders selectable from a codebook in the second group of codebooks based on the second component. Network-side methods are presented, as well as example UEs and network nodes.