A simple-explicit expression for the Laplace transform of rg(r) for 3D square-well quids is proposed. The model is constructed by imposing the following three basic physical requirements : (a) lim(r-->sigma)+g(r)=finite, (b) lim(q-->0)S(q) =finite, and (c) lim(r-->lambda sigma)-g(r)/lim(r-->lambda sigma)+g(r)=exp(epsilon/k(B)T). When applied to 1D square-well quids, the model yields the exact radial distribution function. Furthermore, in the sticky-hard-sphere limit [lambda-->1, epsilon-->infinity, (lambda-1)exp(epsilon/k(B)T)=finite] the model reduces to Baxter’s exact solution of the Percus-Yevick equation. Comparison with Monte Carlo simulation data shows that the model is a good extension of Baxter’s solution to "thin" square-well fluids. For "wide" square-well quids the model is still an acceptable approximation even for densities slightly above the critical density and temperatures slightly below-the critical temperature.