Determining the phylogenetic origin of mitochondria is key to understanding the ancestral mitochondrial symbiosis and its role in eukaryogenesis. However, the precise evolutionary relationship between mitochondria and their closest bacterial relatives remains hotly debated. The reasons include pervasive phylogenetic artefacts, as well as limited protein and taxon sampling. Here, we developed a new model of protein evolution that accommodates both across-site and across-branch compositional heterogeneity. We applied this site-and-branch-heterogeneous model (MAM60 + GFmix) to a considerably expanded dataset that comprises 108 mitochondrial proteins of alphaproteobacterial origin, and novel metagenome-assembled genomes from microbial mats, microbialites, and sediments. The MAM60 + GFmix model fits the data much better and agrees with analyses of compositionally homogenized datasets with conventional site-heterogenous models. The consilience of evidence thus suggests that mitochondria is sister to the Alphaproteobacteria to the exclusion of MarineProteo1 and Magnetococcia. We also show that the ancestral presence of a crista-developing MICOS complex (a Mitofilin domain-containing Mic60) supports this relationship.