  The origin of CP violation is a major mystery, especially in relation to the
strong CP problem. CP being a spontaneously broken symmetry could provide an
elegant solution. However, such models have difficulty making themselves
compatible with low-energy supersymmetry, which is popularly accepted as the
solution to the hierarchy problem. We demonstrate that a certain class of low
scale supersymmetric ``Nelson-Barr'' type models can solve the strong and
supersymmetric CP problems while at the same time generating sufficient weak CP
violation in the $K^{0}-\bar{K}^{0}$ system. Gauge-mediated supersymmetry
breaking is used to provide the needed squark mass degeneracies and $A$-term
proportionalities; though that proves to be still insufficient for a generic
Nelson-Barr model. The workable model we consider here, essentially a
supersymmetric version of the aspon model, has the Nelson-Barr mass texture
enforced by a U(1) gauge symmetry, broken at the TeV scale. The resulting model
is predictive with rich phenomenology soon to be available. Feasibility of the
model considered is established by a detailed renormalization group studies.
