Alignments are a central notion in conformance checking. They establish the best possible connection between an observed trace and a process model, exhibiting the closest model run to the trace. Computing these alignments for huge amounts of traces, coming from big logs, is a computational bottleneck. We show that, for a slightly modified version of the distance function between traces and model runs, we significantly improve the execution time of an A*-based search algorithm. We show experimentally that the alignments found with our modified distance approximate very nicely the optimal alignments for the classical distance.