We study theoretically the bulk modulus (inverse of the compressibility) of a suspension of charged objects (macroions), making use of a cell model to account for the finite density of macroions. The diffuse layer of charged microspecies around a macroion is described by a generic local density functional theory. Within this general framework, we obtain the condition for a positive bulk modulus, which is fulfilled by several proposals made in the literature and rules out the possibility of a critical point. We show that a sufficient condition for a positive compressibility also ensures that the same theory produces repulsive effective pair potentials. (C) 2003 American Institute of Physics.