  We study the localization of gravity on a string-like topological defect
within a 6-dimensional space-time. Assuming zero cosmological constant we find
complete numerical solutions to a set of first-order,
Bogomol'nyi-Prasad-Sommeferld (BPS)-like, equations for the metric and the
scalar field, where the dynamics of the latter are dictated by a
supergravity-type potential. Our axially symmetric solutions have no deficit
angle and factorize as $AdS_5 \times S_1 $ far from the core. They are regular
everywhere, providing complete smooth cigar-like geometries. The total energy
of these configurations depends only on the boundary conditions for the warp
factor and it is shown to vanish.
