Phase unwrapping in the presence of branch points using a least-squares wave-front reconstructor requires the use of a Postprocessing Congruence Operation (PCO). Branch cuts in the unwrapped phase are altered by the addition of a constant parameter h to the rotational component when applying the PCO. Past research has shown that selecting a value of h which minimizes the proportion of irradiance in the pupil plane adjacent to branch cuts helps to maximize performance of adaptive-optics (AO) systems in strong turbulence. In continuation of this objective, this research focuses on optimizing the PCO while accounting for the cumulative effects of the integral control law. Several optimizations are developed and compared using wave-optics simulations. The most successful optimization is shown to reduce the normalized variance of the Strehl ratio across a wide range turbulence strengths and frame rates, including decreases of up to 25 percent when compared to a non-optimized PCO algorithm. AO systems which depend on high, steady Strehl ratio values serve to benefit from these algorithms
