Is there an example of a closed Haken hyperbolic 3-manifold of Heegaard genus 2?



Heegard genus of hyperbolic Haken 3-manifolds
Even better, there are hyperbolic surface bundles with Heegaard genus two. These are all described in Jesse Johnson's paper, titled [Surface bundles with genus two Heegaard splittings](http://arxiv.org/abs/math/0607513). You will need to use some criterion to recognize pseudo-Anosov maps, however. 


