Codimension Two Compactifications and the Cosmological Constant Problem

We consider solutions of six dimensional Einstein equations with two compact dimensions. It is shown that one can introduce 3-branes in this background in such a way that the effective four dimensional cosmological constant is completely independent of the brane tensions. These tensions are completely arbitrary, without requiring any fine tuning. We must, however, fine tune bulk parameters in order to obtain a sufficiently small value for the observable cosmological constant. We comment in the effective four dimensional description of this effect at energies below the compactification scale.