Simulating the hydrodynamics of deformable, floating structures using a partitioned strategy poses a major challenge when the ratio of the added mass to the structural mass is considerate. Existing computational procedures for fluid-structure interaction become less efficient or even unstable. In these situations, it is advisable to modify the coupling to allow the fluid to respond better to the solid motions. A simultaneous solution of the equations governing fluid and solid-body would be a stable choice but is often not feasible. Usually the numerical problems are taken care of with subiterations between fluid and structure, but their convergence can be slow. In this paper we present a more powerful, quasi-simultaneous approach, which tries to mimic a fully simultaneous coupling in an affordable way. It makes use of a simple approximation of the body dynamics, based on the (6 DOF) solid-body modes and the main elastic modes of the structure. The method will be demonstrated in offshore practice, with a falling life boat, a floating CALM buoy, an elastic membrane and a rubber gate.@en