We demonstrate a method that allows a high-efficiency single-photon-avalanche diode (SPAD) with a thick absorption region (> 10 μm) to count single photons at rates significantly higher than previously demonstrated. We apply large (> 30 V) AC bias gates to the SPAD at 1 GHz and detect minute avalanches with a discrimination threshold of 5(1) mV by means of radio-frequency (RF) interferometry. We measure a reduction by a factor of ≈ 500 in the average charge per avalanche when compared to operation in its traditional active-quenching module, and a relative increase of >19 % in detection efficiency at 850 nm. The reduction in charge strongly suppresses self-heating effects in the diode that can degrade performance at high avalanche rates. We show that the single-photon detection system maintains high efficiency at count rates exceeding 108s-1.