Algorithms that minimize putative synapomorphy in an alignment cannot be directly implemented since trivial cases with concatenated sequences would be selected because they would imply a minimum number of events to be explained (e.g., a single insertion/deletion would be required to explain divergence among two sequences). Therefore, indirect measures to approach parsimony need to be implemented. In this paper, we thoroughly present a Global Criterion for Sequence Alignment (GLOCSA) that uses a scoring function to globally rate multiple alignments aiming to produce matrices that minimize the number of putative synapomorphies. We also present a Genetic Algorithm that uses GLOCSA as the objective function to produce sequence alignments refining alignments previously generated by additional existing alignment tools (we recommend MUSCLE). We show that in the example cases our GLOCSA-guided Genetic Algorithm (GGGA) does improve the GLOCSA values, resulting in alignments that imply less putative synapomorphies.