As the raw material for evolution, arbitrary RNA sequences represent the baseline for RNA structure formation and a standard to which evolved structures can be compared. Here, we set out to probe, using physical and chemical methods, the structural properties of RNAs having randomly generated oligonucleotide sequences that were of sufficient length and information content to encode complex, functional folds, yet were unbiased by either genealogical or functional constraints. Typically, these unevolved, nonfunctional RNAs had sequence-specific secondary structure configurations and compact magnesium-dependent conformational states comparable to those of evolved RNA isolates. But unlike evolved sequences, arbitrary sequences were prone to having multiple competing conformations. Thus, for RNAs the size of small ribozymes, natural selection seems necessary to achieve uniquely folding sequences, but not to account for the well-ordered secondary structures and overall compactness observed in nature.