Transformation media designed by standard transformation-optics (TO) approaches, based on real-valued coordinate mapping, cannot exhibit single-negative (SNG) character unless such character is already possessed by the domain that is being transformed. In this paper, we show that, for a given field polarization, pseudo-SNG transformation media can be obtained by transforming a domain featuring double positive (or double-negative) character, via complex analytic continuation of the coordinate transformation rules. Moreover, we apply this concept to the TO-based interpretation of phenomena analogous to the tunnelling effects observable in bi-layers made of complementary epsilon-negative (ENG) and mu-negative (MNG) media, and explore their possible TO-inspired extensions and generalizations.