This paper tackles the problem of finding the optimal non-coherent detector for the reacquisition of weak Global Navigation Satellite System (GNSS) signals in the presence of bits and phase uncertainty. Two solutions are derived based on using two detection frameworks: the Bayesian approach and the generalized likelihood ratio test (GLRT). We also derive approximate detectors of reduced computation complexity and without noticeable performance degradation. Simulation results reveal a clear improvement of the detection probability for the proposed techniques with respect to the conventional detectors implemented in high sensitivity GNSS (HS-GNSS) receivers to acquire weak GNSS signals. Finally, we draw conclusions on which is the best technique to reacquire weak GNSS signals in practice considering a trade-off between performance and complexity.