We study the complexity of term rewrite systems compatible with the Knuth-Bendix order, if the signature of the rewrite system is potentially infinite. We show that the known bounds on the derivation height are essentially preserved, if the rewrite system fulfils some mild conditions. This allows us to obtain bounds on the derivational height of non simply terminating rewrite systems. As a corollary, we re-establish an essentially optimal 2-recursive upper bound on the derivational complexity of finite rewrite systems compatible with a Knuth-Bendix order. Furthermore we link our main result to results on generalised Knuth-Bendix orders and to recent results on transfinite Knuth-Bendix orders. to Alex on this momentous occasion * This work is partly supported by FWF (Austrian Science Fund) project I-603-N18.