  We discuss the regularization of codimension-2 singularities in warped
six-dimensional Einstein-Maxwell axisymmetric models by replacing them by
codimension-1 branes of a ring form, situated around the axis of symmetry.
Further we consider the case of one capped regularized conical brane of
codimension one and study the cosmological evolution which is induced on it as
it moves in between the known {\it static} bulk and cap solutions. We present
the resulting brane Friedmann equation which gives a dominant five-dimensional
$\rho^2$ energy density term at high energies and a term linear to the energy
density at low energies with, however, negative coefficient in the small
four-brane radius limit (i.e. with negative effective Newton's constant)
