The mean first passage time has recently become a useful analytic and computational quantity for estimating reaction rates in many-dimensional activated processes. Unfortunately, the accuracy of this association is limited by the indeterminacy of the appropriate boundary surface with respect to which the first passage times are obtained. The standard choices for this boundary result in an overestimate of the rates in stochastic models using the Langevin equation in the low friction limit. We propose a boundary surface which is a subspace of phase space that results in rates that are accurate in the entire friction regime. It is to be contrasted with equally accurate mean-first-passage-time rates that are obtained using noninvariant subspaces of either the configuration space or phase space and hence are not amenable to nonnumerical analysis. The proposed boundary surface is also shown heuristically and numerically to result from a new kind of variational principle.