The goal of this work is to compare three structural constraints, which differ by the amount of prior information they inject in the joint inversion. One of these constraints is the crossgradient (Gallardo and Meju, 2003) and another two force the gradients to be either parallel or antiparallel, depending on prior information about the sign of velocity-resistivity correlation; one of the constraints also forces the gradients to have identical support. We introduce a flexible framework for 2-D joint inversion, based on Gauss—Newton method, which uses independent meshes for velocity, resistivity and the structural constraint. It is used to compare the considered structural constraints on a synthetic seismic and MT data, simulating a marine subsalt imaging scenario. To study theoretical capabilities of the constraints we first consider a toy “model fusion” example, assuming the true resistivity is known, and then proceed to a more realistic joint inversion experiment. Refs 11. Figs 3.