We construct a family of (p+3)-dimensional brane worlds in which the brane has one compact extra dimension, the bulk has two extra dimensions, and the bulk closes regularly at codimension two submanifolds known as bolts. The (p+1)-dimensional low energy spacetime M_low may be any Einstein space with an arbitrary cosmological constant, the value of the bulk cosmological constant is arbitrary, and the only fields are the metric and a bulk Maxwell field. The brane can be chosen to have positive tension, and the closure of the bulk provides a singularity-free boundary condition for solutions that contain black holes or gravitational waves in M_low. The spacetimes admit a nonlinear gravitational wave whose properties suggest that the newtonian gravitational potential on a flat M_low will behave essentially as the static potential of a massless minimally coupled scalar field with Neumann boundary conditions. When M_low is (p+1)-dimensional Minkowski with p ≥ 3 and the bulk cosmological constant vanishes, this static scalar potential is shown to have the long distance behaviour characteristic of p spatial dimensions.