  We report on an extensive numerical investigation of the Kardar-Parisi-Zhang
equation describing non-equilibrium interfaces. Attention is paid to the
dependence of the growth exponents on the details of the distribution of the
noise. All distributions considered are delta-correlated in space and time, and
have finite cumulants. We find that the exponents become progressively more
sensitive to details of the distribution with increasing dimensionality. We
discuss the implications of these results for the universality hypothesis.
