  In 2001, J. Hempel proved the existence of Heegaard splittings of arbitrarily
high distance by using a high power of a pseudo-Anosov map as the gluing map
between two handlebodies. We show that lower bounds on distance can also be
obtained when using a high power of a suitably chosen Dehn twist. In certain
cases, we can then determine the exact distance of the resulting splitting.
These results can be seen as a natural extension of work by A. Casson and C.
Gordon in 1987 regarding strongly irreducible Heegaard splittings.
