This paper shows that the mean flow of an eddy-permitting model can be altered by assimilationof surface height variability, providing that information about the mean sea surface is included,using an adaption of a statistical-dynamical method devised by Oschlies and Willebrand. Weshow that for a restricted depth range (about 1000 m), dynamical knowledge can make up for thenull space present in surface data whose temporal extent may be too short to distinguish betweenvertical modes. The lack of an accurate geoid has meant that most assimilation methods, whilerepresenting variability well, have been unable to modify the mean flow to any extent. However,we show that by including several approximate forms for the mean sea surface, the mean interiorflow in the upper kilometer can be rapidly adjusted towards reality by the assimilation, with thelocation of major current systems moved by hundreds of kilometers.