  We construct solutions in purely gravitational bulk with flat vacuum branes
without fine tuning the constants of the theory. Our solutions incorporate one
or two branes and have topology S^1 x R^4 without Z_2 symmetry. They are not
invariant under the four-dimensional Lorentz group effectively acting on the
brane, but the significance of this fact will become clear only after the study
of their perturbations.
