Despite substantial work, the phylogeny of malaria parasites remains debated. The matter is complicated by concerns about patterns of evolution in potentially strongly selected genes as well as the extreme AT bias of some Plasmodium genomes. Particularly contentious has been the position of the most virulent human parasite Plasmodium falciparum, whether grouped with avian parasites or within a larger clade of mammalian parasites. Here, we study 3 classes of rare genomic changes, as well as the sequences of mitochondrial ribosomal RNA (rRNA) genes. We report 3 lines of support for a clade of mammalian parasites: 1) we find no instances of spliceosomal intron loss in a hypothetical ancestor of P. falciparum and the avian parasite Plasmodium gallinaceum, suggesting against a close relationship between those species; 2) we find 4 genomic mitochondrial indels supporting a mammalian clade, but none grouping P. falciparum with avian parasites; and 3) slowly evolving mitochondrial rRNA sequences support a mammalian parasite clade with 100% posterior probability. We further report a large deletion in the mitochondrial large subunit rRNA gene, which suggests a subclade including both African and Asian parasites within the clade of closely related primate malarias. This contrasts with previous studies that provided strong support for separate Asian and African clades, and reduces certainty about the historical and geographic origins of Plasmodium vivax. Finally, we find a lack of synapomorphic gene losses, suggesting a low rate of ancestral gene loss in Plasmodium.