We systematically explore the spectrum of gravitational perturbations in codimension-1 DGP braneworlds, and find a 4D ghost on the self-accelerating branch of solutions. The ghost appears for any value of the brane tension, although depending on the sign of the tension it is either the helicity-0 component of the lightest localized massive tensor of mass 0<m^2 < 2H^2 for positive tension, the scalar 'radion' for negative tension, or their admixture for vanishing tension. Because the ghost is

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... vitationally coupled to the brane-localized matter, the self-accelerating solutions are not a reliable benchmark for cosmic acceleration driven by gravity modified in the IR. In contrast, the normal branch of solutions is ghost-free, and so these solutions are perturbatively safe at large distance scales. We further find that when the Z_2 orbifold symmetry is broken, new tachyonic instabilities, which are much milder than the ghosts, appear on the self-accelerating branch. Finally, using exact gravitational shock waves we analyze what happens if we relax boundary conditions at infinity. We find that non-normalizable bulk modes, if interpreted as 4D phenomena, may open the door to new ghost-like excitations.