Is perturbative stability intimately tied with the existence of spacetime fermions in string theory in more than two dimensions? Type 0′B string theory in ten-dimensional flat space is a rare example of a non-tachyonic, non-supersymmetric string theory with a purely bosonic closed string spectrum. However, all known type 0′ constructions exhibit massless NSNS tadpoles signaling the fact that we are not expanding around a true vacuum of the theory. In this note, we are searching for perturbatively stable examples of type 0′ string theory without massless tadpoles in backgrounds with a spatially varying dilaton. We present two examples with this property in non-critical string theories that exhibit four- and six-dimensional Poincaré invariance. We discuss the D-branes that can be embedded in this context and the type of gauge theories that can be constructed in this manner. We also comment on the embedding of these non-critical models in critical string theories and their holographic (Little String Theory) interpretation and propose a general conjecture for the role of asymptotic supersymmetry in perturbative string theory.