Today, negative induced polarization (IP) time-domain responses and responses with non-standard shapes are generally considered as measurement errors and removed in data processing before inversion. However, synthetic and field measurements show that these responses are in fact physically possible and that a simple theoretical explanation of the basic mechanism for their origin can be found by means of superposition of contributions from regions with different sensitivities. The basic mechanism for IP responses with non-standard shapes is investigated by considering the subsurface Cole-Cole parameter sensitivities and time varying IP potential for 2D synthetic models. The time-domain forward response and sensitivities are computed from the finite-element solutions of the frequency-domain differential equation, through a time transformation that takes the current waveform into account. This approach allows for quantitative unbiased estimates of the time-domain responses and sensitivities, which are different from the estimates that can be obtained when using multiple DC forward computations, as often done in the inversion of time-domain IP data. With the increased understanding, previously disregarded IP responses, which can contain valuable information of the subsurface, can be kept for the inversion process and thus contribute to the final parameter distribution.