  We investigate the dynamical stability of warped, axially symmetric
compactifications in anomaly free 6D gauged supergravity. The solutions have
conical defects, which we source by 3-branes placed on orbifold fixed points,
and a smooth limit to the classic sphere-monopole compactification. Like for
the sphere, the extra fields that are generically required by anomaly freedom
are especially relevant for stability. With positive tension branes only, there
is a strict stability criterion (identical to the sphere case) on the charges
present under the monopole background. Thus brane world models with positive
tensions can be embedded into anomaly free theories in only a few ways.
Meanwhile, surprisingly, in the presence of a negative tension brane the
stability criteria can be relaxed. We also describe in detail the geometries
induced by negative tension codimension two branes.
