Multiple sequence alignment is typically the first step in estimating phylogenetic trees, with the assumption being that as alignments improve, so will phylogenetic reconstructions. Over the last decade or so, new multiple sequence alignment methods have been developed to improve comparative analyses of protein structure, but these new methods have not been typically used in phylogenetic analyses. In this paper, we report on a simulation study that we performed to evaluate the consequences of using these new multiple sequence alignment methods in terms of the resultant phylogenetic reconstruction. We find that while alignment accuracy is positively correlated with phylogenetic accuracy, the amount of improvement in phylogenetic estimation that results from an improved alignment can range from quite small to substantial. We observe that phylogenetic accuracy is most highly correlated with alignment accuracy when sequences are most difficult to align, and that variation in alignment accuracy can have little impact on phylogenetic accuracy when alignment error rates are generally low. We discuss these observations and implications for future work.