Conformance checking is a branch of process mining that aims to assess to what degree event data originating from the execution of a (business) process and a corresponding reference model conform to each other. Alignments have been recently introduced as a solution for conformance checking and have since rapidly developed into becoming the de facto standard. The state-of-the-art method to compute alignments is based on solving a shortest path problem derived from the reference model and the event data. Within such a shortest path problem, a cost function is used to guide the search to an optimal solution. The standard cost-function treats mismatches in the model and log as equal. In this paper, we consider a variant of this standard cost function which maximizes the number of correct matches instead. We study the effects of using this cost-function compared to the standard cost function on both small and large models using over a thousand generated and industrial case studies. We further show that the alignment computation process can be sped up significantly in specific instances. Finally, we present a new algorithm for the computation of alignments on models with many log traces that is an order of magnitude faster (in maximizing synchronous moves) compared to the state-of-the-art A* based solution method, as a result of a preprocessing step on the model.