A surface force balance has been used to investigate the viscosity of salt-free (conductivity) water confined between hydrophilic and between hydrophobic surfaces. We examine the process of jump-in, across the last few nanometres of thin water films, to adhesive contact between the surfaces. We analyse the flow of water out of the gap under slip and no-slip boundary conditions at the confining surfaces. In both cases we find that the effective viscosity of water remains comparable to its bulk value even when it is confined to sub-nanometre thin films.