  We show that for any two Heegaard splittings of genus $p$ and $q$ for the
same closed 3-manifold, there is a common stabilization of genus at most 3/2 p
+ 2q - 1. One may compare this to recent examples of Heegaard splittings whose
smallest common stabilizations have genus at least $p+q$ or $p + 1/2 q$
depending on the notion of equivalence.
