Simplifying the weft hierarchy

We give simple, self-contained proofs of the basic hardness results for the classes Wt]$Wt]$ of the weft hierarchy. We extend these proofs to higher levels of the hierarchy and illuminate the distinctions among its classes. The anti-monotone collapse at W1,s]$W1,s]$ and the normalization of weft-t$t$ formulas arise as by-products of the proofs.