The sound transmission loss (TL) characteristics of panel constructions with thin face sheets and a thicker, lighter core are investigated. Analytical models of TL are developed for constructions with isotropic and orthotropic core materials. The occurrence of acoustic coincidence is described for symmetric and antisymmetric modes of propagation, in the panel. Symmetric propagation involves thickness deformation of the core, while antisymmetric propagation involves a bending deformation of the panel without thickness deformation. For symmetric modes, coincidence occurs near the conventional double wall resonance frequency characterized by the stiffness of the core and the mass of the face sheets, and also at higher frequencies associated with bending wave propagation in the face sheets. Antisymmetric modes account for shear deformation in the core, which results in a softening of the bending rigidity of the panel at higher frequencies. For orthotropic core materials, the acoustic behavior is dependent on the direction of propagation over the surface of the panel. Measured TL results for representative panels show good agreement with predictions. Finally, a procedure for obtaining improved TL performance is described, which involves shifting the double wall resonance to below the frequency band of interest, and limiting the shear stiffness of the core to shift the onset of bending wave coincidence to higher frequencies. Greater than mass law TL, similar to that of conventional double wall constructions, can be achieved over a significant frequency band in the audio range. The mechanical integrity of the panel is provided by the shear stiffness of the core.