In this paper, we present a method to design low-power low-voltage current-mirror based integrators for continuous-time Sigma-Delta modulators. It is shown that, by proper biasing of the mirror transistors, very high modulation index can be achieved at low-voltage supply. Careful analysis of the current-mode integrator shows that there exists an optimum supply voltage for minimum power consumption. Simulation results show that proper choice of the supply voltage can reduce the power consumption of the integrator by 40%.