  We consider `brane universe' scenarios with standard-model fields localized
on a 3-brane in 6 spacetime dimensions. We show that if the spacetime is
rotationally symmetric about the brane, local quantities in the bulk are
insensitive to the couplings on the brane. This potentially allows
compactifications where the effective 4-dimensional cosmological constant is
independent of the couplings on the 3-brane. We consider several possible
singularity-free compactification mechanisms, and find that they do not
maintain this property. We also find solutions with naked spacetime
singularities, and we speculate that new short-distance physics can become
important near the singularities and allow a compactification with the desired
properties. The picture that emerges is that standard-model loop contributions
to the effective 4-dimensional cosmological constant can be cut off at
distances shorter than the compactification scale. At shorter distance scales,
renormalization effects due to standard-model fields renormalize the 3-brane
tension, which changes a deficit angle in the transverse space without
affecting local quantities in the bulk. For a compactification scale of order
10^{-2} mm, this gives a standard-model contribution to the cosmological
constant in the range favored by cosmology.
