We propose and evaluate a method for significantly compressing modal sound models, thereby making them far more practical for audiovisual applications. The dense eigenmode matrix, needed to compute the sound model's response to contact forces, can consume tens to thousands of megabytes depending on mesh resolution and mode count. Our eigenmode compression pipeline is based on non-linear optimization of Moving Least Squares (MLS) approximations. Enhanced compression is achieved by exploiting symmetry both within and between eigenmodes, and by adaptively assigning per-mode error levels based on human perception of the far-field pressure amplitudes. Our method provides smooth eigenmode approximations, and efficient random access. We demonstrate that, in many cases, hundredfold compression ratios can be achieved without audible degradation of the rendered sound.