The synthesis of broad-beam radiation patterns with increased angular rejection and bandpass filtering functionalities from a rectilinear leaky-wave antenna is proposed. A sharpened angular filter response is obtained with shorter antennas, by introducing radiation nulls adjacent to a synthesized broadbeam. Moreover, exploiting the inherent dispersive properties of LWAs, aforementioned features can be combined with bandpass frequency filtering characteristics. These angular and bandpass filtering functionalities are validated with experiments performed on fabricated prototypes in modulated substrate integrated waveguide (SIW) technology. An enhancement in the angular rejection from 1 dB/ to 2.5 dB/ is demonstrated for a 200-long antenna with a broad main beam covering the range [20, 40] at 15 GHz, and with a simultaneous bandpass in the [14GHz, 19 GHz] band.