A derivation relation is a total regulator on ,~* if, for every language L~ ,~*, the set of all words derivable from L is a regular language. We show that for a wide class of derivation relations =~*, =O~ is a total regulator on ,Y* if and only if it is a well-quasi-order (wqo) on ,Y*. Using wqo theory, we give a characterization of all non-erasing pure context-free (0S) derivation relations which ate total regulators.