  In the context of the Randall-Sundrum braneworld, the minimal geometric
deformation approach (MGD) is used to generate a new physically acceptable
interior solution to Einstein's field equations for a spherically symmetric
compact distribution. This new solution is used to elucidate the role of
exterior Weyl stresses from bulk gravitons on compact stellar distributions. We
found strong evidences showing that the exterior dark radiation ${\cal U}^+$
always increases both the pressure and the compactness of stellar structures,
and that the exterior "dark pressure" ${\cal P}^+$ always reduces them.
