Open boundary conditions (OBCs) should give low artificial reflection of outgoing waves. Most OBCs proposed in the literature try to take into account the fact that the phase velocity of these waves is a priori unknown. However, an even more important problem is the presence of a "slow mode", i.e. a quasi-stationary geostropphic flow, at the open boundary. This geostrophic flow should be separated from the superimposed waves constructing rhe OBC. It is also important to write the OBC on integrated form, in order to obtain a well-posed problem and avoid model drift. Two new conditions are derived using these ideas, and are show to perform better than previous conditions.