In this joint work in progress with Alex Massarenti we study the following problem; given a complex variety V with transversal rational double points as singularities, find conditions that ensure that all infinitesimal deformations are locally trivial. This extends previous joint work which (building on corresponding result by Paul Hacking for the moduli stacks) showed that the coarse moduli space of \bar M_{g,n} has no nontrivial infinitesimal deformations, except if (g,n)=(1,2).