We report a theoretical investigation on the possibilities and trade-offs when tapering a bi-directional fed leaky-wave antenna (LWA) to reduce the side lobes level, when operating with the two opposite antenna ports. It is demonstrated that, for high radiation efficiency designs, the directivity can be distorted due to low aperture illumination efficiency if the LWA is not symmetrically tapered with an adequate modulation function. The theory is corroborated with simulations of modulated LWAs in substrate integrated technology.