  Let $f: S^1\to S^1$ be a $C^3$ homeomorphism without periodic points having a
finite number of critical points of power-law type. In this paper we establish
real a-priori bounds, on the geometry of orbits of $f$, which are beau in the
sense of Sullivan, i.e. bounds that are asymptotically universal at small
scales. The proof of the beau bounds presented here is an adaptation, to the
multicritical setting, of the one given by the second author and de Melo, for
the case of a single critical point.
