Repetitive extragenic palindrome (REP)-associated tyrosine transposase enzymes (RAYTs) bind REP DNA domains and catalyze their cleavage. Genomic sequence analyses identify potential noncoding REP sequences associated with RAYT-encoding genes. To probe the conformational space of potential RAYT DNA binding domains, we report here spectroscopic and calorimetric measurements that detect and partially characterize the solution conformational heterogeneity of REP oligonucleotides from six bacterial species. Our data reveal most of these REP oligonucleotides adopt multiple conformations, suggesting that RAYTs confront a landscape of potential DNA substrates in dynamic equilibrium that could be selected, enriched, and/or induced via differential binding. Thus, the transposase-bound DNA motif may not be the predominant conformation of the isolated REP domain. Intriguingly, for several REPs, the circular dichroism spectra suggest guanine tetraplexes as potential alternative or additional RAYT recognition elements, an observation consistent with these REP domains being highly nonrandom, with tetraplex-favoring 5'-G and 3'-C-rich segments. In fact, the conformational heterogeneity of REP domains detected and reported here, including the formation of noncanonical DNA secondary structures, may reflect a general feature required for recognition by RAYT transposases. Based on our biophysical data, we propose guanine tetraplexes as an additional DNA recognition element for binding by RAYT transposase enzymes.