  We study a model Dyson-Schwinger equation for the quark propagator closed
using an {\it Ansatz} for the gluon propagator of the form \mbox{$D(q) \sim
q^2/[(q^2)^2 + b^4]$} and two {\it Ans\"{a}tze} for the quark-gluon vertex: the
minimal Ball-Chiu and the modified form suggested by Curtis and Pennington.
Using the quark condensate as an order parameter, we find that there is a
critical value of $b=b_c$ such that the model does not support dynamical chiral
symmetry breaking for $b>b_c$. We discuss and apply a confinement test which
suggests that, for all values of $b$, the quark propagator in the model {\bf is
not} confining. Together these results suggest that this Ansatz for the gluon
propagator is inadequate as a model since it does not yield the expected
behaviour of QCD.
