  Necessary conditions are proposed for the admissibility of singular classical
solutions with 3+1-dimensional Poincare invariance to five-dimensional gravity
coupled to scalars. Finite temperature considerations and examples from AdS/CFT
support the conjecture that the scalar potential must remain bounded above for
a solution to be physical. Having imposed some restrictions on naked
singularities allows us to comment on a recent proposal for solving the
cosmological constant problem.
