A novel, accurate and fast full-wave method has been applied for the analysis and design of a printed-circuit laterally-shielded slotted leaky-wave antenna. Important higher order phenomena, like coupling with channel guide leaky-modes, finite stub height and dispersion effects occurring with wide slots, have been taken into account. By comparisons with curves obtained using an approximate transverse resonance equation, it has been shown that it is necessary to take these effects into account for a correct analysis. To achieve greater gains, the substrate-superstrate configuration has been added to the original leaky-wave antenna. The resonance conditions have been checked, obtaining a minimum of leakage rate, which confirms the relationship of maximum gain with the excitation of weakly attenuated leaky-waves.