This work explores coded caching in the symmetric K-user cache-aided MISO BC with imperfect CSIT-type feedback, for the specific case where the cache size is much smaller than the library size. Building on the recently explored synergy between caching and delayed-CSIT, and building on the tradeoff between caching and CSIT quality, the work proposes new schemes that boost the impact of small caches, focusing on the case where the cumulative cache size is smaller than the library size. This small-cache setting places an additional challenge due to the fact that some of the library content must remain entirely uncached, which forces us to dynamically change the caching redundancy to compensate for this. Our proposed scheme is near-optimal, and the work identifies the optimal cache-aided degrees-of-freedom (DoF) performance within a factor of 4.