  We prove that the Julia set $J(f)$ of at most finitely renormalizable
unicritical polynomial $f:z\mapsto z^d+c$ with all periodic points repelling is
locally connected. (For $d=2$ it was proved by Yoccoz around 1990.) It follows
from a priori bounds in a modified Principle Nest of puzzle pieces. The proof
of a priori bounds makes use of new analytic tools developed in math.DS/0505191
that give control of moduli of annuli under maps of high degree.
