Simple tandemly organized (GTG)n/(CAC)n sequences are spread throughout the human chromosomes. The most informative DNA fingerprints for the testing of pedigrees and/or paternity were obtained with the simple triplet repeat probe (GTG)5 or its complement (CAC)5. These hypervariable simple-repeat fragments are stably inherited in a Mendelian fashion. Using these highly discriminating probes, all human individuals could, theoretically, be differentiated, except for genetically identical monozygotic twins. Examples from actual case work are reported and pertinent advantages of this methodology are discussed.