  In this paper we give a combinatorial description of the renormlization
limits of infinitely renormalizable unimodal maps with {\it essentially
bounded} combinatorics admitting quadratic-like complex extensions. As an
application we construct a natural analogue of the period-doubling fixed point.
Dynamical hairiness is also proven for maps in this class. These results are
proven by analyzing {\it parabolic towers}: sequences of maps related either by
renormalization or by {\it parabolic renormalization}.
