Due to the longer PRN code employed in next-generation GNSS (Global Navigation Satellite System), receivers in the signal acquisition process should test a larger number of code phase hypotheses. Recently, to reduce acquisition time and computational complexity, TDCC (Two-dimensional Compressed Correlator) is introduced, and this technique is different from the conventional double dwell search technique in terms of parameters used to reduce acquisition time and computational complexity. Studies for optimizing the performance of TDCC have not been introduced yet, therefore, in this paper, detection thresholds of TDCC are investigated to optimize its acquisition performance. The optimal detection thresholds minimizing the MAT (Mean Acquisition Time) and MAC (Mean Acquisition Computation) are numerically evaluated and analyzed for widely used detection strategies in its serial and parallel search schemes. It is demonstrated that the minimized MAT and MAC are much smaller than the MAT and MAC using a detection threshold based on CFAR (Constant False Alarm Rate).