We present a study of the properties of the host galaxies of unusual transient objects of two types, both being sub-luminous compared with the major classes of supernovae. Those of one type exhibit unusually strong calcium features, and have been termed 'Ca-rich'. Those of the second type, with SN2002cx as the prototype and SN2008ha as the most extreme example to date, have some properties in common with the first, but show typically lower ejecta velocities, and different early spectra. We confirm important differences in the environments of the two types, with the Ca-rich transients preferentially occurring in galaxies dominated by old stellar populations. Quantitatively, the association of the the Ca-rich transients with regions of ongoing star formation is well matched to that of type Ia supernovae. The SN2002cx-like transients are very different, with none of the present sample occurring in an early-type host, and a statistical association with star-formation regions similar to that of type II-P supernovae, and therefore a delay time of 30-50 Myrs.