  We investigate the prospects for neutralino dark matter within the
Supersymmetric Standard Model (SSM) including the constraints from universal
soft supersymmetry breaking and radiative breaking of the electroweak symmetry.
The latter is enforced by using the one-loop Higgs effective potential which
automatically gives the one-loop corrected Higgs boson masses. We perform an
exhaustive search of the allowed five-dimensional parameter space and find that
the neutralino relic abundance $\Omega_\chi h^2_0$ depends most strongly on the
ratio $\xi_0\equiv m_0/m_{1/2}$. For $\xi_0\gg1$ the relic abundance is almost
always much too large, whereas for $\xi_0\ll1$ the opposite occurs. For
$\xi_0\sim1$ there are wide ranges of the remaining parameters for which
$\Omega_\chi\sim1$. We also determine that $m_{\tilde q}\gsim250\GeV$ and
$m_{\tilde l}\gsim100\GeV$ are necessary in order to possibly achieve
$\Omega_\chi\sim1$. These lower bounds are much weaker than the corresponding
ones derived previously when radiative breaking was {\it not} enforced.
