  We consider compactifications of six dimensional gravity in four dimensional
Minkowski or de Sitter space times a two dimensional sphere, S^2. As has been
recently pointed out, it is possible to introduce 3-branes in these backgrounds
with arbitrary tension without affecting the effective four dimensional
cosmological constant, since its only effect is to induce a deficit angle in
the sphere. We show that if a monopole like configuration of a 6D U(1) gauge
field is used to produce the spontaneous compactification of the two extra
dimensions in a sphere a fine tuning between brane and bulk parameters is
reintroduced once the quantization condition for the gauge field is taken into
account, so the 4D cosmological constant depends on the brane tension. This
problem is absent if instead of the monopole we consider a four form field
strength in the bulk to obtain the required energy-momentum tensor. Also,
making use of the four form field, we generalize the solution to an arbitrary
number of dimensions (\ge 6), keeping always four noncompact dimensions and
compactifying the rest in a n-dimensional sphere. We show that a (n+1)-brane
with arbitrary tension can be introduced in this background without affecting
the effective 4D cosmological constant.
