  We discuss the linearized, gravitational self-interaction of a brane of
arbitrary codimension in a spacetime of arbitrary dimension. We find that in
the codimension two case the gravitational self-force is exactly zero for a
Nambu-Goto equation of state, generalizing a previous result for a string in
four dimensions. For the case of a 3-brane, this picks out the case of a
six-dimensional brane-world model as having special properties which we
discuss. In particular, we see that bare tension on the brane has no effect
locally, suppressing the cosmological constant problem.
