  We solve a model of phase separation among two competing phases frustrated by
the long-range Coulomb interaction in two and three dimensions (2D/3D) taking
into account finite compressibility effects. In the limit of strong frustration
in 2D, we recover the results of R. Jamei, S. Kivelson, and B. Spivak, Phys.
Rev. Lett. 94, 056805 (2005) and the system always breaks into domains in a
narrow range of densities, no matter how big is the frustration. For weak
frustration in 2D and for arbitrary frustration in 3D the finite
compressibility of the phases is shown to play a fundamental role. Our results
clarify the different role of screening in 2D and 3D systems. We discuss the
thermodynamic stability of the system near the transition to the phase
separated state and the possibility to observe it in real systems.
