We study two-phase displacement via the steady compression of an air reservoir connected to an oilfilled capillary tube. Our experiments and modeling reveal complex displacement dynamics depending on compression rate and reservoir volume that, for large reservoirs, depend on a single dimensionless compressibility number. We identify two distinct displacement regimes, separated by a critical value of the compressibility number. While the subcritical regime exhibits quasisteady displacement after an initial transient, the supercritical regime exhibits burstlike expulsion.