We propose here a methodology for improving mass-conservation features of the fractional-step schemes on moving grids applied to viscous incompressible flows containing free surfaces. The idea is to find a better approximation for the intermediate velocity. This is achieved by using a prediction upon the end-of-step pressure in the pressure gradient term of the fractional momentum equation. Thus, an intermediate velocity results being much closer to the final one, than that of the standard fractional step scheme. We propose a methodology, where this goal can be achieved without necessitating to resolve any additional linear system.