Many widely-used statistical packages and recent authors addressing process capability apply Cpmin cases where tolerances are asymmetric. This can misrepresent process capability, andpoints to the need to apply appropriate capability measures in the asymmetric case. We compare andcontrast six relatively unfamiliar capability indices appropriate for asymmetric tolerances to givethem greater visibility and to help potential users choose among them. For some of these indicesmethods of estimation from process data have not been published; work on this is deferred to subsequent papers