Network nodes, wireless devices and methods of reducing signaling overhead are provided. In one embodiment, a method includes transmitting to the wireless device at least one power threshold parameter to be used by the wireless device to determine a number of beams to be included in a multi-beam precoder codebook and transmitting to the wireless device a signal to interference plus noise ratio (SINR) to be used by the wireless device to determine to use one of a single beam precoder and a multiple beam precoder.