It is well-known that perfect channel state information (CSI) at the transmitter and the receiver (CSIT/CSIR) can be used to decompose a multi- antenna channel into a bank of parallel channels. While perfect CSIR maybe a reasonable assumption for practical systems, perfect CSIT is generally difficult to achieve. Recent attention in communication systems design has thus shifted towards limited feedback schemes where partial CSI is fed back from the receiver to the transmitter. In this work, we consider a precoding scheme which excites a subset of the transmit dimensions with independent data. The main focus is on systematic quantized precoder designs that bridge the gap between statistical precoding and perfect CSIT precoding in spatially correlated channels. In this work, we propose an asymptotic perturbation theory-inspired codebook design obtained from a quantization of the local neighborhood around the statistically dominant precoding direction(s). This design is implemented in practice by maps that can rotate and shrink sets on the Grassmannian manifold. Numerical results show substantial gains can be achieved with the proposed design over statistical precoding.