  We study the localization of gravity on string-like defects in codimension
two. We point out that the gravity-localizing `local cosmic string' spacetime
has an orbifold singularity at the horizon. The supergravity embedding and the
AdS/CFT correspondence suggest ways to resolve the singularity. We find two
resolutions of the singularity that have a semiclassical gravity description
and study their effect on the low-energy physics on the defect. The first
resolution leads, at long distances, to a codimension one Randall-Sundrum
scenario. In the second case, the infrared physics is like that of a
conventional finite-size Kaluza-Klein compactification, with no power-law
corrections to the gravitational potential. Similar resolutions apply also in
higher codimension gravity-localizing backgrounds.
