  We perform a nonperturbative tuning of the coefficients in the $O(a^2)$
improved action for staggered fermions. The mass splitting for the pions of
different doubler flavor is used as a measure of the symmetry breaking effects
introduced by $O(a^2)$ discretization errors. We find that the flavor
nondegeneracy can be somewhat reduced but not eliminated by such a tuning,
indicating the need for new terms in the action to reduce the nondegeneracy.
