It is generally believed that the coupling of energy between the solar wind and the magnetosphere depends almost exclusively on the solar wind speed and magnetic field, with density and temperature playing little or no role. However, recent studies have indicated that under certain conditions, such as the main phase of a storm, density can have a significant role in modulating the transfer of energy to the magnetosphere. In this paper we demonstrate the effect using global MHD simulations of the solar wind-magnetosphere interaction. We also identify the physical mechanism that leads to the density control, namely the modification of the compression ratio of the bow shock, and explain why it is only apparent during periods of strong, southward IMF.