Using new integral field observations of 106 galaxies in three nearby clusters, we investigate how the intrinsic scatter of the Fundamental Plane depends on the way in which the velocity dispersion and effective radius are measured. Our spatially resolved spectroscopy, combined with a cluster sample with negligible relative distance errors, allows us to derive a Fundamental Plane with minimal systematic uncertainties. From the apertures we tested, we find that velocity dispersions measured within a circular aperture with radius equal to one effective radius minimizes the intrinsic scatter of the Fundamental Plane. Using simple yet powerful Jeans dynamical models, we determine dynamical masses for our galaxies. Replacing luminosity in the Fundamental Plane with dynamical mass, we demonstrate that the resulting Mass Plane has further reduced scatter, consistent with zero intrinsic scatter. Using these dynamical models, we also find evidence for a possibly non-linear relationship between dynamical mass-to-light ratio and velocity dispersion.