Using a 7-dimensional unbinned likelihood fitter, we optimize decay amplitudes describing e-exp(+) e-exp(-) -> psi(2S) -> pi pi J psi; J/psi -> e-exp(+) e-exp(-), Mu-exp(+) Mu-exp(-) in 696,000 signal events collected by the CLEO-c detector at the Cornell Electron Storage Ring. The Kappa Model, which assumes a double gluon E1 X E1 operator and low-energy pion constraints, has an optimal value of kappa = 0.2740 +/- 0.0006stat +/- 0.0009sys but fails conservative chi-exp(2) tests on histograms of projected quantities. Fitting three other models, one with final state interactions between the pions, one with exp(3)S-sub(1) - exp(3)D-sub(1) mixing and M1 X M1 gluons, and one with only pion constraints, moderately reduces chi-exp(2) values. After a restriction to delta m-sub(spin) = 0 transitions, we fit for the magnitude of the D/S amplitude ratio in bins of mass(pi pi). Fits for the corresponding phase are not reliable due to a lack of sensitivity. Disallowing this phase while still assuming delta m-sub(spin) = 0 , we fit a quasi model-independent parameterization and obtain our best fit quality.