Lower critical solution temperatures (LCST)-type of phase diagrams, including the presence of closed loops, have been encountered for the first time in binary and quasi-binary liquid solutions of ionic liquids. Furthermore, the results constitute the first experimental support for the existence of a theoretically postulated, but never encountered, special kind of type VII phase diagram. Two distinct mechanisms are involved in the appearance of demixing upon temperature increase. These findings underlie the presence of specific, oriented interactions between the ionic liquid, 1-alkyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}amide, [Cnmim][NTf2], and trichloromethane, as well as aggregation phenomena.