  We point out several subtleties arising in brane-world scenarios of
cosmological constant cancellation. We show that solutions with curvature
singularities are inconsistent, unless the contribution to the effective
four-dimentional cosmological constant of the physics that resolves the
singularities is fine-tuned. This holds for both flat and curved branes.
Irrespective of this problem, we then study an isolated class of flat solutions
in models where a bulk scalar field with a vanishing potential couples to a
3-brane. We give an example where the introduction of a bulk scalar potential
results in a nonzero cosmological constant. Finally we comment on the stability
of classical solutions of the brane system with respect to quantum corrections.
