  In the Cascading Gravity brane-world scenario, our 3-brane lies within a
succession of lower-codimension branes, each with their own induced gravity
term, embedded into each other in a higher-dimensional space-time. In the
6+1-dimensional version of this scenario, we show that a 3-brane with tension
remains flat, at least for sufficiently small tension that the weak-field
approximation is valid. The bulk solution is nowhere singular and remains in
the perturbative regime everywhere.
