  We describe static, brane--like, solutions to vacuum Einstein's equations in
D = n + m + 2 dimensional spacetime with m \ge 2 and n \ge 1. These solutions
have positive ADM mass but no horizon. The curvature invariants are finite
everywhere except at r = 0 where r is the radial coordinate in the m + 1
dimensional space. The presence of n \ge 1 extra dimensions is crucial for
these properties. Such solutions may be naturally anticipated if Mathur's
fuzzball proposal for black holes is correct.
