  Supersymmetric model contributions to the neutron electric dipole moment
arise via quark electric dipole moment operators, whose matrix elements are
usually calculated using the Naive Quark Model (NQM). However, experiments
indicate that the NQM does not describe well the quark contributions $\Delta q$
to the nucleon spin, and so may provide misleading estimates of electric dipole
operator matrix elements. Taking the $\Delta q$ from experiment, we indeed find
consistently smaller estimates of the neutron electric dipole moment for given
values of the supersymmetric model parameters. This weakens previous
constraints on CP violation in supersymmetric models, which we exemplify
analytically in the case where the lightest supersymmetric particle (LSP) is a
$U(1)$ gaugino $\tilde{B}$, and display numerically for other LSP candidates.
