We consider an infinite-volume brane world setup where a codimension one-br
ane is coupled to bulk gravity plus a scalar field with vanishing potential
. The latter is protected by bulk supersymmetry, which is intact even if br
ane supersymmetry is completely broken as the volume of the extra dimension
is infinite. Within this setup we discuss a flat solution with a "self-tun
ing" property, i.e. such a solution exists for a continuous range of values
for the brane tension. This infinite-volume solution is free of any singul
arities, and has the property that the brane cosmological constant is prote
cted by bulk supersymmetry. We, however, also point out that consistency of
the coupling between bulk gravity and brane matter generically appears to
require that the brane world-volume theory be conformal.