  We derive some new conditions for integrability of dynamically defined C^1
invariant splittings in arbitrary dimension and co-dimension. In particular we
prove that every 2-dimensional C^1 invariant decomposition on a 3-dimensional
manifold satisfying a volume domination condition is uniquely integrable. In
the special case of volume preserving diffeomorphisms we show that standard
dynamical domination is already sufficient to guarantee unique integrability.
