Here, we study connections between (quasi-equationally) critical and relatively sub-directly irreducible members of [finitely-generated] quasi-varieties [subsuming those between former ones and critical sets and enabling one to reduce the task of finding latter ones to that of former ones, the usefulness of which is then demonstrated by applying it to quasi-varieties of {De} Morgan lattices, the finite lattice of which was found in an earlier work of ours].