Our compressed haplotype selection techniques are essential for TX-Phase's computational efficiency. We compare TX-Phase (compressed) with an alternative side-channel resilient implementation without compression (original), which more closely follows SHAPEIT4's approach, with respect to their running times. We report the per-sample running time for phasing Chromosome 20 using the UKB data set across varying reference panel sizes. The results are summarized for different components of the algorithm, including PBWT querying (A) and haplotype filtering (B), as well as the full phasing pipeline (C). Our compressed algorithms substantially reduce the running time of TX-Phase, which otherwise becomes prohibitive for large reference panels.