  We compute how threshold effects obtained by integrating out a heavy particle
localized on a codimension-2 brane influence the properties of the brane and
the bulk fields it sources in D=d+2 dimensions. We do so using a recently
developed formalism for matching the characteristics of higher codimension
branes to the properties of the bulk fields they source. We show that although
the dominant dependence on a heavy mass M that is induced in the low-energy
codimension-2 tension has the generic size expected, T_2 \propto M^d, the
very-low-energy effective potential governing the on-brane curvature once bulk
KK modes are integrated out can be additionally suppressed, by factors of order
k^2 M^d, where k is the bulk gravitational coupling. In the special case of a
codimension-2 brane in a 6D supersymmetric bulk we also estimate the size of
the contributions of short-wavelength bulk loops near the brane, and find these
can be similarly suppressed.
