  We show that the set of cusp shapes of hyperbolic tunnel number one manifolds
is dense in the Teichmuller space of the torus. A similar result holds for
tunnel number n manifolds. As a consequence, for fixed n, there are infinitely
many hyperbolic tunnel number n manifolds with at most one exceptional Dehn
filling. This is in contrast to large volume Berge knots, which are tunnel
number one manifolds, but with cusp shapes converging to a single point in
Teichmuller space.
