  We give another proof of a theorem of Scharlemann and Tomova and of a theorem
of Hartshorn. The two theorems together say the following. Let M be a compact
orientable irreducible 3--manifold and P a Heegaard surface of M. Suppose Q is
either an incompressible surface or a strongly irreducible Heegaard surface in
M. Then either the Hempel distance d(P) <= 2 genus(Q) or P is isotopic to Q.
This theorem can be naturally extended to bicompressible but weakly
incompressible surfaces.
