The present invention describes methods of identifying altered recombinases and compositions thereof, wherein at least one amino acid is different from a parent, wild-type recombinase and the altered recombinase has improved recombination efficiency towards wild-type and/or pseudo att site sequences relative to the parent, wild-type recombinase. The present invention also includes methods of modifying the genomes of cells using the altered recombinases, including methods of site-specifically integrating a polynucleotide sequence of interest in a genome of a eucaryotic cell.