From the abstract for "Going nuclear: gene family evolution and vertebrate phylogeny reconciled":
Gene duplications have been common throughout vertebrate evolution, introducing paralogy and so complicating phylogenetic inference from nuclear genes. Reconciled trees are one method capable of dealing with paralogy, using the relationship between a gene phylogeny and the phylogeny of the organisms containing those genes to identify gene duplication events. This allows us to infer phylogenies from gene families containing both orthologous and paralogous copies. Vertebrate phylogeny is well understood from morphological and palaeontological data, but studies using mitochondrial sequence data have failed to reproduce this classical view.The abstract continues to save the day: "Reconciled tree analysis of a database of 118 vertebrate gene families supports a largely classical vertebrate phylogeny." In other words, reconciled tree analysis picks the tree that contains the fewest departures/epicycles from the phylogenetic picture from morphology and paleontology.