  All ultrafilters under consideration here are non-principal ultrafilters on
the set omega of natural numbers. We are concerned with the possible
cofinalities of ultrapowers of omega with respect to such ultrafilters. We show
that no cardinal below the groupwise density number g can occur as such a
cofinality and that at most one cardinal below the splitting number s can so
occur. The proof for s, when combined with a result of Nyikos, gives the
additional information that all P_{kappa}-point ultrafilters, for kappa greater
than the bounding number b, are nearly coherent.
