Brillouin scattering-based distributed fiber-optic sensing is a powerful measurement tool that uses the inelastic scattering of incident light by an acoustic wave (phonon) to determine strain and/or temperature conditions of the fiber. Since the original Brillouin-time-domain-analysis (BOTDA) technique was proposed, several other analysis methods have been introduced to improve sensing performance in four key areas: spatial resolution; measurement accuracy; total sensing length; and measurement-acquisition time. The four factors are generally interrelated and improvements to one factor often come at the cost of one or more of the others. For example, one system might sacrifice spatial resolution for total sensing length, while another might sacrifice accuracy to gain acquisition speed. We present a BOTDA system based on dark-pulse scattering that provides improved resolution, accuracy, and acquisition time over conventional BOTDA systems, without the severe limitations on sensing length often imposed by other high-resolution techniques. Theoretical validation of the method is given, and experimental results are presented that demonstrate 20-mm resolution strain measurements with an accuracy of plusmn20 muepsiv, which is the highest spatial resolution yet reported for a BOTDA system