  This Note provides first a generalization of the stabilization result of
Eisenbud and Ulrich for the regularity of powers of a m-primary ideal to the
case of ideals that are not generated in a single degree. We then partially
extend our previous results expressing this stabilization degree in term of the
regularity of a specific graded strand of the Rees ring : The natural extension
of the statement holds at least if the stabilization index or the regularity is
greater than the number of variables. In any case a precise comparison is
given.
