Superconducting nanowire single photon detectors are typically biased using a constant current source and shunted in a conductance which is over an order of magnitude larger than the peak normal domain conductance of the detector. While this design choice is required to ensure quenching of the normal domain, the use of a small load resistor limits the pulse amplitude, rising-edge slew rate, and recovery time of the detector. Here, we explore the possibility of actively quenching the normal domain, thereby removing the need to shunt the detector in a small resistance. We first consider the theoretical performance of an actively quenched superconducting nanowire single photon detector and, in comparison to a passively quenched device, we predict roughly an order of magnitude improvement in the slew rate and peak voltage achieved in this configuration. The experimental performance of actively and passively quenched superconducting nanowire single photon detectors are then compared. It is shown that, in comparison to a passively quenched device, the actively quenched detectors simultaneously exhibited improved count rates, dark count rates, and timing jitter.