For elastic materials containing fluid-saturated porosity, the pore compressibility is a measure of the deformation of a unit pore volume in response to a change in fluid pressure. Rather than being measured, this quantity has been routinely set equal to an effective solid compressibility, since this equality is exact whenever a single solid component is present. However, we show that the pore compressibility and solid compressibility may be uncorrelated in general. In certain special circumstances they do not even share the same sign. Although thermodynamic and mechanical stability constraints cause solid and drained-frame bulk moduli of a porous composite to be positive and bounded by component properties, the pore compressibility is unconstrained and, therefore, can have negative values. For special realizable model materials, the value of the pore compressibility can be found using an exact expression valid for a composite made up of one fluid and two solid components, i.e., two porous components. In order to quantify how various factors affect the sign and magnitude of the pore compressibility, pore compressibilities were calculated for models that used two porous components having the microgeometry of an assemblage of concentric spheres. This model implicitly assumes the pores are on a much smaller length scale than the concentric spheres. Modeling results show that with the stiffer porous material forming the outer shells of the concentric spheres, the pore compressibility of such materials is negative when solid component bulk moduli differ by at least a factor of 5, if, in addition, the porosities and drained frame moduli of the two porous components are relatively low. Negative pore compressibilities were found for realizable models whose two porous constituents had the properties of silicon nitride and either sandstone or clay. For models using combinations of alumina and glass foam properties, pore compressibilities were non-negative but smaller than the compressibilities of the solid components.