The simple compression of a planetary magnetosphere by varying solar wind stagnation pressure is limited by currents induced in the electrically conducting parts of the planet. This inhibition is especially important for Mercury, since the radius of the electrically conducting iron core is a large fraction of the planetary radius, which in turn is a significant fraction of the subsolar magnetospheric radius b. Previous treatments of solar wind standoff distance variations at Mercury using the terrestrial analogue b6 assumption have neglected this phenomenon. Using the lowest suggested value of the planetary dipole moment, 2.4¿1022 G cm3, we estimate that a minimum pressure of ~38P0 where P0 is the external stagnation pressure in the steady state, is required to force the standoff distance down to the subsolar surface of Mercury if the pressure change persists for at least 1 day. This value is 4.3 times that which would be predicted if Mercury had no core, and it is larger than the maximum pressure predicted at Mercury's orbit (~25P0) on the basis of hourly averaged solar wind statistics at 1 AU. Thus a direct interaction at any time of solar wind plasma with the surface of Mercury due to external compression effects alone is unlikely for solar wind conditions similar to those at present.