Stimulated Brillouin scattering (SBS) in optical fibers has long been used in frequency-selective optical signal processing, including in the realization of microwave-photonic (MWP) filters. In this work, we report a significant enhancement in the selectivity of SBS-based MWP filters. Filters having a single passband of 250 MHz–1 GHz bandwidth are demonstrated, with selectivity of up to 44 dB. The selectivity of the filters is better than that of the corresponding previous arrangements by about 15 dB. The shape factor of the filters, defined as the ratio between their -20 dB bandwidth and their -3 dB bandwidth, is between 1.35 and 1.5. The central transmission frequency, bandwidth, and spectral shape of the passband are all independently adjusted. Performance enhancement is based on two advances, compared with previous demonstrations of tunable SBS-basedMWPfilters: (a) the polarization attributes of SBS in standard, weakly birefringent fibers are used to discriminate between in-band and out-of-band components and (b) a sharp and uniform power spectral density of the SBS pump waves is synthesized through external modulation of an optical carrier by broadband, frequency-swept waveforms. The signal-to-noise ratio of filtered radio-frequency waveforms and the linear dynamic range of the filters are estimated analytically and quantified experimentally. Lastly, a figure of merit for the performance of the filters is proposed and discussed. The filters are applicable to radio-over-fiber transmission systems.