Open boundary conditions (OBCs) should give small artificial reflection of outgoing waves. Most OBCs proposed in the literature are designed to cope with the fact that the phase velocity of these waves is in general unknown. However, an even more important problem is the presence of a slow mode, i.e., a quasi-stationary geostrophic flow, at the open boundary. This geostrophic flow should be separated from the superimposed waves when constructing the OBC. It is also important to write the OBC on integrated form, to avoid model drift and make sure that the correct solution is approached asymptotically. New conditions are derived using these ideas. Several OBCs are tested in one-dimensional and two-dimensional numerical simulations. The new conditions are found to perform better than the previous ones.