Flat Vacuum Branes Without Fine Tuning

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.