Conventional deformation mechanism (DM) maps are constructed for single-valued grain size. When diffusional creep is competitive with power law creep, such maps are a poor guide to rheology and microstructure development in distributed grain size materials because the strain rate dependence on grain size implies wide variations in local stress and/or strain rate. We present DM maps for quartzite with realistic grain size distributions using two bounding models: (1) homogeneous strain rate with local stress varying from grain to grain and (2) homogeneous stress with local stain rate varying. Distributed grain size systems are stronger at low stresses and have larger power law creep fields and larger regions where two or more mechanisms contribute significantly to the total strain rate. Our DM maps do not incorporate grain shape and packing, but we review theoretical work on the effects of these variables and compare rheological predictions with our own for the development of idealized core-and-mantle microstructure.