  We examine spacetimes which generalize Lifshitz scaling to allow hyperscaling
violation invariance (i.e. a constant conformal transformation) for the types
of singularities frequently found in the Lifshitz case. We find that most of
these spacetimes suffer either from a traditional naked curvature singularity
or a null curvature singularity robust against stringy higher derivative
corrections. We do find a one-parameter family that evades these issues but
this family requires exotic matter, in particular involving a negative energy
density that may not be interpreted as due to a cosmological constant.
