Phase resonances in compound gratings are studied in the frequency and time domains, with the gratings having two dissimilar grooves within the unit cell that each support waveguide cavity modes that couple. Described in this work are the dependence of the phase resonances' Q on the degree of difference between the grooves in the unit cell, their optical properties, a closed-form expression describing their dispersion, their excitation, and the extraction of energy from the phase resonances into free space and into a waveguide. Application to optical filters and corrugated surface antennas are discussed.