We report on the use of hydrostatic pressure, P, to deswell thermosensitive poly(N-isopropylacrylamide) (pNIPAM) microgels and show that it can affect the polymer-solvent mixing as much as temperature, which is the traditional variable used to deswell pNIPAM particles. Interestingly, the microgel volume changes more gradually with pressure than it does with temperature. By comparing the pressure and temperature induced deswelling, we obtain the pressure dependence of the Flory solvency parameter, X; it increases with P, indicating that pressure decreases the polymer-solvent miscibility. We interpret this increase in terms of the entropy change, Delta S, when a polymer-solvent contact is broken to form a solvent-solvent contact and find that vertical bar Delta S vertical bar also increases with P, consistent with previous experimental results with polymers and other gels. Hydrostatic pressure thus changes the entropic contribution of mixing, causing X to increase and ultimately leading to particle deswelling.