h-Cobordisms between simply connected 4-manifolds

h-cobordisms between simply connected 4-manifolds are studied. It is shown that most inertial h-cobordisms have a handle decomposition with one 2-handle and one 3-handle, and h-cobordisms between nondiffeomorphic manifolds have handle decompositions with the minimal number of handles consistent with a diffeomorphism between the stabilized ends. Also the number of distinct h-cobordisms between two fixed manifolds is described in terms of isomorphisms of their quadratic forms. These results are applied to Dolgachev surfaces and the Kummer surface using recent work of Donaldson, Friedman and Morgan, and Matumoto.