The current molecular data explosion poses new challenges for large-scale phylogenomic analyses that can comprise hundreds or even thousands of genes. A property that characterizes phylogenomic datasets is that they tend to be gappy, i.e. can contain taxa with (many and disparate) missing genes. In current phylogenomic analyses, this type of alignment gappyness that is induced by missing data frequently exceeds 90%. We present and implement a generally applicable mechanism that allows for reducing memory footprints of likelihood-based [maximum likelihood (ML) or Bayesian] phylogenomic analyses proportional to the amount of missing data in the alignment. We also introduce a set of algorithmic rules to efficiently conduct tree searches via subtree pruning and re-grafting moves using this mechanism.