It is well known that a persistent southward Interplanetary Magnetic Field (IMF) produces increased geomagnetic activity. It has recently been shown that a sudden increase in solar wind pressure results in poleward expansion of the auroral oval and closing of the polar cap over a wide range of MLTs, and this effect is more pronounced under southward IMF orientation. We show that southward IMF conditions combined with high solar wind dynamic pressure immediately after a pressure front impact lead to enhanced coupling between the solar wind and the terrestrial magnetosphere, significantly increasing the geoeffectiveness of the solar wind. We evaluate geoeffectiveness by the coupling efficiency, defined as the ratio of the cross-polar-cap potential measured by Defense Meteorological Satellite Program (DMSP) spacecraft to the cross-magnetospheric potential calculated using solar wind parameters. We examine changes in the size of the polar cap and the coupling efficiency for a number of solar wind pressure enhancements under southward IMF configuration. We confirm the previously observed closing of the polar cap and show that there is a simultaneous increase of the coupling efficiency. This increase is measured for all cases, despite the fact that the magnetosphere is greatly compressed, and the increase is measured even when the solar wind electric field is reduced.