  We study integer coefficient polynomials of fixed degree and maximum height
$H$, that are irreducible by Dumas's criterion. We call such polynomials Dumas
polynomials. We derive upper bounds on the number of Dumas polynomials, as $H$
approaches infinity. We also show that, for a fixed degree, the density of
Dumas polynomials in all irreducible integer coefficient polynomials is
strictly less than 1.
