We describe a gated Geiger-mode single-photon avalanche diode (SPAD) detection system in which both gating and avalanche discrimination are implemented by coherent addition of discrete harmonics of the fundamental gate frequency. With amplitude and phase control for each harmonic at the cathode, we form <340 ps bias gates, and with similar control at the anode we cancel the gate transient with >65 dB suppression, allowing avalanche-discrimination thresholds at the anode below 2 mV or <8 fC. The low threshold not only accurately discriminates diminutive avalanches but also achieves usable detection efficiencies with lower total charge, reducing the afterpulse probability and allowing the use of gate pulses that exceed the SPAD breakdown voltage by more than 10 V, both of which increase detection efficiency. With detection efficiency of 0.19 +/- 0.01, we measure per-gate afterpulse probability below 6.5 x 10(-4) after 3.2 ns, and with detection efficiency of 0.51 +/- 0.02 we measure per-gate afterpulse probability below 3.5 x 10(-3) after 10 ns. (C) 2013 AIP Publishing LLC.