In our previous note, we discussed some problems that can arise when using standard principal components analysis (specifically, principal components regression) to model the relationship between independent (x) and dependent (y) variables. In this note, we present some dimensionality reduction techniques that alleviate some of those problems, in particular what we call Y-Aware Principal Components Analysis, or Y-Aware PCA. We will use our variable treatment package vtreat in the examples we show in this note, but you can easily implement the approach independently of vtreat.