A method at a second device of indicating a recommended precoder matrix to a first device, said method comprising: estimating channel conditions with respect to said first device; determining factorized precoder feedback based at least in part on said channel conditions, wherein said factorized precoder feedback indicates at least one of a recommended conversion precoder matrix and a recommended tuning precoder matrix, said recommended conversion and tuning precoder matrices jointly representing a recommended precoder matrix that is a matrix multiplication of the recommended conversion and tuning precoder matrices, and wherein said recommended conversion precoder matrix restricts a number of channel dimensions considered by said recommended tuning precoder matrix and said recommended tuning precoder matrix matches said recommended precoder matrix to an effective channel between said first and second devices that is defined in part by said recommended conversion precoder matrix; sending said factorized precoder feedback to said first device to indicate said recommended precoder matrix to said first device; and characterized by further comprising maintaining a two-dimensional table of precoder matrices, each one for selection as said recommended precoder matrix, and wherein each row or column of said table corresponds to a particular one in a plurality of conversion precoder matrices and each column or row of said table corresponds to a particular one in a plurality of tuning precoder matrices, and wherein said factorized precoder feedback comprises at least one of a row index value and a column index value, for identifying a particular one of said precoder matrices as said recommended precoder matrix. estimating channel conditions with respect to said first device; determining factorized precoder feedback based at least in part on said channel conditions, wherein said factorized precoder feedback indicates at least one of a recommended conversion precoder matrix and a recommended tuning precoder matrix, said recommended conversion and tuning precoder matrices jointly representing a recommended precoder matrix that is a matrix multiplication of the recommended conversion and tuning precoder matrices, and wherein said recommended conversion precoder matrix restricts a number of channel dimensions considered by said recommended tuning precoder matrix and said recommended tuning precoder matrix matches said recommended precoder matrix to an effective channel between said first and second devices that is defined in part by said recommended conversion precoder matrix; sending said factorized precoder feedback to said first device to indicate said recommended precoder matrix to said first device; and characterized by further comprising maintaining a two-dimensional table of precoder matrices, each one for selection as said recommended precoder matrix, and wherein each row or column of said table corresponds to a particular one in a plurality of conversion precoder matrices and each column or row of said table corresponds to a particular one in a plurality of tuning precoder matrices, and wherein said factorized precoder feedback comprises at least one of a row index value and a column index value, for identifying a particular one of said precoder matrices as said recommended precoder matrix.