Brane-world singularities are analysed, emphasizing the case of supergravity in singular spaces where the singularity puzzle is naturally resolved. These naked singularities are either time-like or null, corresponding to the finite or infinite amount of conformal time that massless particles take in order to reach them. Quantum mechanically we show that the brane-world naked singularities are inconsistent. Indeed we find that time-like singularities are not wave-regular, so the time-evolution of wave packets is not uniquely defined in their vicinity, while null singularities absorb incoming radiation. Finally we stress that for supergravity in singular spaces there is a topological obstruction, whereby naked singularities are necessarily screened off by the second boundary brane.