Among several structured light approaches, phase shift is the most widely adopted in real-world 3D reconstruction devices. This is mainly due to its high accuracy, strong resilience to noise and straightforward implementation. However, Phase shift also exhibits an inherent weakness, that is the spatial ambiguity resulting from the periodicity of the sinusoidal wave adopted. Of course many phase unwrapping methods have been proposed to solve such ambiguity. One of the most promising methods exploits additional signals of mutually prime periods, in order to observe a distinct combination of phases for each spatial point. Unfortunately, for such combination to be properly recognized, a very high accuracy in phase recovery must be attained for each signal. In fact, even modest errors could lead to unwrapping faults, making the overall approach much less resilient to noise than plain phase shift. With this paper we introduce a feasible and effective fault recovery method that can be directly applied to multi-period phase shift. The combined pipeline offers an optimal accuracy and coverage even with high noise conditions, overcoming the setbacks of the original method. The performance of such pipeline is established by means of an in depth set of experimental evaluations and comparison, both with real and synthetically generated data.