Abstract: We propose a novel solid/fluid coupling method that treats the coupled system in a fully implicit manner making it stable for arbitrary time steps, large density ratios, etc. In contrast to previous work in computer graphics, we derive our method using a simple back-of-the-envelope approach which lumps the solid and fluid momenta together, and which we show exactly conserves the momentum of the coupled system. Notably, our method uses the standard Cartesian fluid discretization and does not require (moving) conforming tetrahedral meshes or ALE frameworks. Furthermore, we use a standard Lagrangian framework for the solid, thus supporting arbitrary solid constitutive models, both implicit and explicit time integration, etc. The method is quite general, working for smoke, water, and multiphase fluids as well as both rigid and deformable solids, and both volumes and thin shells. Rigid shells and cloth are handled automatically without special treatment, and we support fully one-sided discretizations without leaking. Our equations are fully symmetric, allowing for the use of fast solvers, which is a natural result of properly conserving momentum. Finally, for simple explicit time integration of rigid bodies, we show that our equations reduce to form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though four spatial dimensions rather than three.