Afterpulsing was investigated experimentally in an InGaAs single-photon avalanche diode (SPAD) operating in the biasing and sensing regime of periodic-gating techniques. These techniques support single-photon counting at rates in the 100MHz range with low afterpulse probability and are characterized by sub-nanosecond active gates that limit total avalanche-charge flows to the 100 fC range or less. We achieved comparable gating and sensing performance with a system using non-periodic gates and were able to make traditional double-pulse afterpulse measurements from 4.8 ns to 2 mu s in this new low-avalanche-current regime. With 0.50 ns gate duration and a detection efficiency of 0.15 at 1310nm the per-gate afterpulse probability at 4.8 ns is 0.008, while with a 1.5 ns gate it is almost two orders of magnitude higher. We provide a quantitative connection between afterpulse probability and total avalanche charge, and between the performance observed in traditional gating techniques for InGaAs SPADs and those observed with periodic gating techniques.