In this paper, we discuss different options for quantized feedback and feedback reduction for a precoded spatial-multiplexing multiple-input multiple-output (MIMO) system in a time-varying channel. The novel contributions of this paper are a quantized feedback strategy based on the bit-error-rate (BER) of a linear receiver, and two new feedback reduction strategies for a time-varying channel. Both these feedback reduction schemes exploit the time correlation of the MIMO channel. They basically can be viewed as an optimized generalization of existing feedback reduction strategies.