  It is shown that the gauge theory of relativistic 3-Branes can be formulated
in a conformally invariant way if the embedding space is six-dimensional. The
implementation of conformal invariance requires the use of a modified measure,
independent of the metric in the action. Brane-world scenarios without the need
of a cosmological constant in 6D are constructed. Thus, no ``old'' cosmological
constant problem appears at this level.
