The projection of magnetospheric regions into the dayside ionosphere as determined by particle precipitation characteristics was studied for dependence on solar wind parameters. It was found that the solar wind kinetic pressure p dramatically affected the map of magnetospheric projections. Under the constraint that p ≥ 4 nPa (yielding <p> = 5.9 nPa), the area of the cusp (magnetic latitude times magnetic local time extent) was 4.83 degree-hours; whereas under the constraint that p ≤ 2 nPa (yielding <p> = 1.5 nPa), the cusp area was only 1.01 degree-hours. The ionospheric footprint of the low-latitude boundary layer was similarly affected. Various possible correlations of p with other solar wind variables, including n, υ, and |Bz|, proved unable to account for the pressure effect. Because one criterion for identifying the cusp is high fluxes, the effect of nυ was investigated with particular care, both in examples and statistically. Again, p itself had by far the most striking effect. Thus we concluded that some physical mechanism is needed to account for the pressure effect. One possibility is that increased direct solar wind plasma penetration of the magnetopause occurs under high-p conditions in the manner suggested by various proponents of impulsive penetration models. An alternative, which we find promising, is that, regardless of the original interplanetary magnetic field (IMF) strength, a high-p solar wind leads to a large compression factor for the magnetosheath field, which is the field actually in contact with the magnetosphere. From this latter viewpoint, the chief effect of high particle pressure is simply to enhance the effectiveness of the interaction of the IMF with the magnetosphere.