  We derive a prediction of dynamical tunneling rates from regular to chaotic
phase-space regions combining the direct regular-to-chaotic tunneling mechanism
in the quantum regime with an improved resonance-assisted tunneling theory in
the semiclassical regime. We give a qualitative recipe for identifying the
relevance of nonlinear resonances in a given $\hbar$-regime. For systems with
one or multiple dominant resonances we find excellent agreement to numerics.
