In recent years, the security of avalanche photodiodes as single photon detectors for quantum key distribution has been subjected to much scrutiny. The most prominent example of this surrounds the vulnerability of such devices to blinding under strong illumination. We focus on self-differencing avalanche photodiodes, single photon detectors that have demonstrated count rates exceeding 1 GCounts/s resulting in secure key rates over 1 MBit/s. These detectors use a passive electronic circuit to cancel any periodic signals thereby enhancing detection sensitivity. However this intrinsic feature can be exploited by adversaries to gain control of the devices using illumination of a moderate intensity. Through careful experimental examinations, we define here a set of criteria for these detectors to avoid such attacks.