A method of precoding transmissions from a first device to a second device, said method comprising: receiving factorized precoder feedback from the second device indicating at least one of a recommended conversion precoder matrix and a recommended tuning precoder matrix that jointly represent a recommended precoder matrix that is a matrix multiplication of the recommended conversion and tuning precoder matrices, 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 that is defined in part by said recommended conversion precoder matrix; determining a precoding operation based at least in part on evaluating said recommended precoder matrix; transmitting a precoded signal to the second device that is precoded according to said precoding operation; characterized by maintaining one or more codebooks as a two-dimensional table of precoder matrices, 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 in said table as said recommended precoder matrix; and futher comprising maintaining one or more codebooks of conversion precoder matrices and tuning precoder matrices, and wherein each conversion precoder matrix has row-column dimensions of N T x k, where the number of rows N T equals a number of transmit antenna ports at the first device and the number of columns k equals a conversion dimension that is less than the value of N T; and wherein said recommended tuning matrix has dimension k x r, where r is a transmission rank used by the first device, and wherein N T, k and r are related as N T ≥ k ≥ r to thereby restrict the number of channel dimensions considered by said recommended tuning precoder matrix. receiving factorized precoder feedback from the second device indicating at least one of a recommended conversion precoder matrix and a recommended tuning precoder matrix that jointly represent a recommended precoder matrix that is a matrix multiplication of the recommended conversion and tuning precoder matrices, 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 that is defined in part by said recommended conversion precoder matrix; determining a precoding operation based at least in part on evaluating said recommended precoder matrix; transmitting a precoded signal to the second device that is precoded according to said precoding operation; characterized by maintaining one or more codebooks as a two-dimensional table of precoder matrices, 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 in said table as said recommended precoder matrix; and futher comprising maintaining one or more codebooks of conversion precoder matrices and tuning precoder matrices, and wherein each conversion precoder matrix has row-column dimensions of N T x k, where the number of rows N T equals a number of transmit antenna ports at the first device and the number of columns k equals a conversion dimension that is less than the value of N T; and wherein said recommended tuning matrix has dimension k x r, where r is a transmission rank used by the first device, and wherein N T, k and r are related as N T ≥ k ≥ r to thereby restrict the number of channel dimensions considered by said recommended tuning precoder matrix.