We recently showed that Saccharomyces cerevisiae telomeric DNA can fold into an unprecedented pseudocircular G-hairpin (PGH) structure. However, the formation of PGHs in the context of extended sequences, which is a prerequisite for their function in vivo and their applications in biotechnology, has not been elucidated. Here, we show that despite its 'circular' nature, PGHs tolerate single-stranded (ss) protrusions. High-resolution NMR structure of a novel member of PGH family reveals the atomistic details on a junction between ssDNA and PGH unit. Identification of new sequences capable of folding into one of the two forms of PGH helped in defining minimal sequence requirements for their formation. Our time-resolved NMR data indicate a possibility that PGHs fold via a complex kinetic partitioning mechanism and suggests the existence of K+ ion-dependent PGH folding intermediates. The data not only provide an explanation of cation-type-dependent formation of PGHs, but also explain the unusually large hysteresis between PGH melting and annealing noted in our previous study. Our findings have important implications for DNA biology and nanotechnology. Overrepresentation of sequences able to form PGHs in the evolutionary-conserved regions of the human genome implies their functionally important biological role(s).