  We extend a recently discovered, non-singular 6 dimensional brane, solution
to D=4+n dimensions. As with the previous 6D solution the present solution
provides a gravitational trapping mechanism for fields of spin 0, 1/2, 1 and 2.
There is an important distinction between 2 extra dimensions and $n$ extra
dimensions that makes this more than a trivial extension. In contrast to
gravity in n >2 dimensions, gravity in n=2 dimensions is conformally flat. The
stress-energy tensor required by this solution has reasonable physically
properties, and for n=2 and n=3 can be made to asymptotically go to zero as one
moves away from the brane.
