For any finite group G G and any prime p p one can ask which ordinary irreducible representations remain irreducible in characteristic p p , or more generally, which representations remain homogeneous in characteristic p p . In this paper we address this question when G G is a proper double cover of the symmetric or alternating group. We obtain a classification when p = 3 p=3 except in the case of a certain family of partitions relating to spin RoCK blocks. Our techniques involve induction and restriction, degree calculations, decomposing projective characters and recent results of Kleshchev and Livesey on spin RoCK blocks.