DNA regions which are composed of a single or relatively few short sequence motifs usually in tandem ('pure simple sequences') have been reported in the genomes of diverse species, and have been implicated in a range of functions including gene regulation, signals for gene conversion and recombination, and the replication of telomeres. They are thought to accumulate by DNA slippage and mispairing during replication and recombination or extension of single-strand ends. In order to systematize the range of DNA simplicity and the genetic nature of the regions that are simple, we have undertaken an extensive computer search of the DNA sequence library of the European Molecular Biology Laboratory (EMBL). We show here that nearly all possible simple motifs occur 5-10 times more frequently than equivalent random motifs. Furthermore, a new computer algorithm reveals the widespread occurrence of significantly high levels of a new type of 'cryptic simplicity' in both coding and noncoding DNA. Cryptically simple regions are biased in nucleotide composition and consist of scrambled arrangements of repetitive motifs which differ within and between species. The universal existence of DNA simplicity from monotonous arrays of single motifs to variable permutations of relatively short-lived motifs suggests that ubiquitous slippage-like mechanisms are a major source of genetic variation in all regions of the genome, not predictable by the classical mutation process.