Abundant novel circular Rep-encoding ssDNA viruses (CRESS DNA viruses) have been discovered in the past decade, prompting a new appreciation for the ubiquity and genomic diversity of this group of viruses. Although highly divergent in the hosts they infect or are associated with, CRESS DNA viruses are united by the homologous replication-associated protein (Rep). An accurate genealogy of Rep can therefore provide insights into how these diverse families are related to each other. We used a dataset of eukaryote-associated CRESS DNA RefSeq genomes (n=926), which included representatives from all six established families and unclassified species. To assure an optimal Rep genealogy, we derived and tested a bespoke amino acid substitution model (named CRESS), which outperformed existing protein matrices in describing the evolution of Rep. The CRESS model-estimated Rep genealogy resolved the monophyly of Bacilladnaviridae and the reciprocal monophyly of Nanoviridae and the alpha-satellites when trees estimated with general matrices like LG did not. The most intriguing, previously unobserved result is a likely single origin of intron-containing Reps, which causes several geminivirus genera to group with Genomoviridae (bootstrap support 55%, aLRT SH-like support 0.997, 0.91-0.997 in trees estimated with established matrices). This grouping, which eliminates the monophyly of Geminiviridae, is supported by both domains of Rep, and appears to be related to our use of all RefSeq Reps instead of subsampling to get a smaller dataset. In addition to producing a trustworthy Rep genealogy, the derived CRESS matrix is proving useful for other analyses; it best fit alignments of capsid protein sequences from several CRESS DNA families and parvovirus NS1/Rep sequences.