Codebook design for limited feedback Spatial Multiplexing commonly relies on the assumption of i.i.d. Rayleigh fading. It is well known that realistic MIMO channels may exhibit large correlation and/or dominant components and that antennas could be dual-polarized. Hence there is much appeal to come up with design criteria that can cope with such a large distribution of propagation conditions. In this paper, efficient ways to design high-performance and low-complexity codebooks for limited feedback-based Spatial Multiplexing evolving in various environments are provided. In particular, new design criteria are derived for transmit correlated and dual-polarized scenarios. Some of the codebook structures derived in this paper are components of the codebooks accepted in 3GPP LTE. Simulation examples are provided to confirm the proposed criteria.