We argue that the brane-world picture with matter-fields confined to 4-d domain walls and with gravitational interactions across the bulk disallows adding an arbitrary constant to the low-energy, 4-d effective theory -- which finesses the usual cosmological constant problem. The analysis also points to difficulties in stabilizing moduli fields; as an alternative, we suggest scenarios in which the moduli motion is heavily damped by various cosmological mechanisms and varying ultra-slowly with time.