We report on a gated single-photon detector based on InGaAs/InP avalanche photodiodes (APDs) with a single-photon detection efficiency exceeding 55% at 1550 nm. Our detector is gated at 1 GHz and employs the self-differencing technique for gate transient suppression. It can operate nearly dead time free, except for the one clock cycle dead time intrinsic to self-differencing, and we demonstrate a count rate of 500 Mcps. We present a careful analysis of the optimal driving conditions of the APD measured with a dead time free detector characterization setup. It is found that a shortened gate width of 360 ps together with an increased driving signal amplitude and operation at higher temperatures leads to improved performance of the detector. We achieve an afterpulse probability of 7% at 50% detection efficiency with dead time free measurement and a record efficiency for InGaAs/InP APDs of 55% at an afterpulse probability of only 10.2% with a moderate dead time of 10 ns.