  We present metric solutions in six and higher dimensions with a bulk
cosmological constant, where gravity is localized on a 3-brane. The corrections
to four-dimensional gravity from the bulk continuum modes are power-law
suppressed. Furthermore, the introduction of a bulk ``hedgehog'' magnetic field
leads to a regular geometry, and can localize gravity on the 3-brane with
either positive, zero or negative bulk cosmological constant.
