  We discuss brane world sum rules for compactifications involving an arbitrary
number of spacetime dimensions. One of the most striking results derived from
such consistency conditions is the necessity for negative tension branes to
appear in five-dimensional scenarios. We show how this result can be evaded for
brane world models with more than five dimensions. As an example, we consider a
novel realization of the Randall-Sundrum scenario in six dimensions involving
only positive tension branes. A complete account of our results appeared in
hep-th/0106140.
