  We use thin position of Heegaard splittings to give a new proof of Haken's
Lemma that a Heegaard surface of a reducible manifold is reducible and of
Scharlemann's ``Strong Haken Theorem'', that a Heegaard surface for a
3-manifold may be isotoped to intersect a given collection of essential spheres
and discs in a single loop each. This article could also serve as an
introduction to the theory of generalized Heegaard surfaces and it includes a
careful study of their behaviour under amalgamation.
