Abstract Lead halide perovskites often suffer from a strong hysteretic behavior on their j?V response in photovoltaic devices that has been correlated with slow ion migration. The electron extraction layer has frequently been pointed to as the main culprit for the observed hysteretic behavior. In this work three hole transport layers are studied with well-defined highest occupied molecular orbital (HOMO) levels and interestingly the hysteretic behavior is markedly different. Here it is shown that an adequate energy level alignment between the HOMO level of the extraction layer and the valence band of the perovskite, not only suppresses the hysteresis, avoiding charge accumulation at the interfaces, but also degradation of the hole transport layer is reduced. Numerical simulation suggests that formation of an injection barrier at the organic/perovskite heterointerface could be one mechanism causing hysteresis. The suppression of such barriers may require novel design rules for interface materials. Overall, this work highlights that both external contacts need to be carefully optimized in order to obtain hysteresis-free perovskite devices.