Single-stranded (ss) transposition, a recently identified mechanism adopted by members of the widespread IS200/IS605 family of insertion sequences (IS), is catalysed by the transposase, TnpA. The transposase of IS608, recognizes subterminal imperfect palindromes (IP) at both IS ends and cleaves at sites located at some distance. The cleavage sites, C, are not recognized directly by the protein but by short sequences 5′ to the foot of each IP, guide (G) sequences, using a network of canonical (‘Watson–Crick’) base interactions. In addition a set of non-canonical base interactions similar to those found in RNA structures are also involved. We have reconstituted a biologically relevant complex, the transpososome, including both left and right ends and TnpA, which catalyses excision of a ss DNA circle intermediate. We provide a detailed picture of the way in which the IS608 transpososome is assembled and demonstrate that both C and G sequences are essential for forming a robust transpososome detectable by EMSA. We also address several questions central to the organization and function of the ss transpososome and demonstrate the essential role of non-canonical base interactions in the IS608 ends for its stability by using point mutations which destroy individual non-canonical base interactions.