  Cosmic censorship is known to fail in some well-controlled phenomena, calling
into question the predictive power of General Relativity and opening up the
possibility of observing Planck-scale physics. We propose that the cosmic
censorship conjecture can be amended so that its spirit prevails. Naked
singularities that, classically, have zero mass are allowed. Physically, these
are Planck-sized `black holes', which evaporate in a few Planck times. General
Relativity fails only for a tiny interval in time, to then quickly regain
control in a Miltonian evolution that returns us to the predictive paradise of
Einstein's equations. If this refinement of the conjecture is correct, then,
even though Nature does allow to expose breakdowns in the smooth fabric of
spacetime, it limits them to a mostly harmless minimum.
