The traditional approaches to predict entrainment of circadian clocks by light are based on 2 concepts that were never successfully unified: the non-parametric approach assumes that entrainment occurs via discrete daily phase shifts while the parametric approach assumes that entrainment involves changes of the clock's velocity. Here the authors suggest a new approach to predict and model entrainment. Unlike the traditional approaches, it does not assume a priori the mechanism of how the internal and external cycle lengths are matched (via phase shifts, velocity changes, or even other mechanisms). It is based on a circadian integrated response characteristic (CIRC) that describes how the circadian system integrates light signals at different circadian phases, without specifying exactly when and how fast its progression is affected. Light around subjective dawn compresses the internal cycle; light around subjective dusk expands it. While the phase response curve (PRC) describes the results of experiments using light stimuli (of specified duration and intensity), the CIRC reflects how the system integrates any given light profile, be it single pulses or any form of light-dark cycle (from skeleton photoperiods to natural light profiles). CIRCs are characterized by their shape (determining the extent of their dead zone) and their asymmetry (the ratio of its compressing and expanding portions). They are dimensionless (time/time), and their maximum is by definition 1. To make predictions about entrainment, the CIRC is multiplied with the light intensity/sensitivity at any given time point. Unlike the PRC and the velocity response curve, the CIRC can be assessed on the basis of entrained steady states, by modeling experimental results. The CIRC approach makes several predictions that can be tested experimentally.