In this paper we show for the first time how sedimentary rocks above a salt diapir can deform in either a brittle or a viscous way depending on the stress state and strain rates. Most existing models for salt tectonics incorporate only one or other of these deformation mechanisms resulting in different conclusions. Taking as an example the controversial problem of buoyant salt diapirism, we demonstrate how diapirs can grow in an overburden which may deform by both creep and faulting. We argue that salt movement can take place under low differential stresses because sediments may deform by pressure-solution creep. These zones of diffuse deformation co-exist with faults where differential stresses are high enough to reach the yield limit at which sediments fail. We demonstrate two conditions under which buoyant diapirs can cause substantial faulting in their overburden without the application of tectonic forces. Buoyant diapirs can fault overburdens with high viscosity contrast (μoverburden/μsalt > 102) if the topographic relief they induce in the surface is removed by rapid erosion.