Light shifts are known to be an important limitation to the mid- A nd long-term fractional frequency stability of different types of atomic clocks. In this article, we demonstrate the experimental implementation of an anti-light-shift interrogation protocol onto a continuous-wave (cw) microcell atomic clock based on coherent population trapping (CPT). The method, inspired by the autobalanced Ramsey spectroscopy technique demonstrated in pulsed atomic clocks, consists in the extraction of atomic based information from two successive light-shifted clock frequencies obtained at two different laser-power values. Two error signals, computed from the linear combination of signals acquired along a symmetric sequence, are managed in a dual-loop configuration to generate a clock frequency free from light shift. Using this method, the sensitivity of the clock frequency to both laser-power and microwave-power variations can be reduced by more than an order of magnitude compared to normal operation. In the present experiment, the consideration of the nonlinear light-shift dependence allows enhancement of the light-shift mitigation. The implemented technique allows an improvement of the clock Allan deviation for time scales higher than 1000 s. This method can be applied in various kinds of atomic clocks such as CPT-based atomic clocks, double-resonance Rb clocks, or cell-stabilized lasers.