  Colding and Gabai have given an effective version of Li's theorem that
non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard
splittings. As a corollary of their work, we show that Haken hyperbolic
3-manifolds have a finite collection of strongly irreducible Heegaard surfaces
$S_i$ and incompressible surfaces $K_j$ such that any strongly irreducible
Heegaard surface is a Haken sum $S_i + \sum_j n_j K_j$, up to one-sided
associates of the Heegaard surfaces.
