In considering the best possible solutions for answering phylogenetic questions from genomic sequences, we have chosen a strategy that we suggest is superior to others that have gone previously. We have ignored multigene families and instead have used single-gene families. This minimizes the inadvertent analysis of paralogs. We have employed strict data controls and have reasoned that if a protein is not capable of recovering the uncontroversial parts of a phylogenetic tree, then why should we use it for the more controversial parts? We have sliced and diced the data in as many ways as possible in order to uncover the signals in that data. Using this strategy, we have tested two controversial hypotheses concerning eukaryotic phylogenetic relationships: the placement of arthropoda and nematodes and the relationships of animals, plants, and fungi. We have constructed phylogenetic trees from 780 single-gene families from 10 completed genomes and amalgamated these into a single supertree. We have also carried out a total evidence analysis on the only universally distributed protein families that can accurately reconstruct the uncontroversial parts of the phylogenetic tree: a total of five families. In doing so, we ignore the majority of single-gene families that are universally distributed as they do not have the appropriate signals to recover the uncontroversial parts of the tree. We have also ignored every protein that has ever been used previously to address this issue, simply because none of them meet our strict criteria. Using these data controls, site stripping, and multiple analyses, 24 out of 26 analyses strongly support the grouping of vertebrates with arthropods (Coelomata hypothesis) and plants with animals. In the other two analyses, the data were ambivalent. The latter finding overturns an 11-year theory of Eukaryotic evolution; the first confirms what has already been said by others. In the light of this new tree, we re-analyze the evolution of intron gain and loss in the rpL14 gene and find that it is much more compatible with the hypothesis presented here than with the Opisthokonta hypothesis.