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A hybrid technique that combines eigenfunction expansions with direct singular integral equation methods is used for the exact analysis of parallel plate-fed slot antennas loaded by dielectric-coated perfectly conducting strips. The primary excitation may be either a TE/TM incident mode of the parallel-plate waveguide or an incident E-/H-polarized plane wave. The problem is formulated in terms of a set of singular integral or integrodifferential equations of the first kind, which are discretized using quasianalytical methods. The matrix elements of the resulting system of linear algebraic equations are given either in closed form or via rapidly converging series. This, in conjunction with the small matrix size required, enables one to obtain very accurate results with low computational cost.