In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with $\textit {essentially bounded}$ 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 $\textit {parabolic towers}$: sequences of maps related either by renormalization or by $\textit {parabolic renormalization}$.