  Models of strongly correlated electrons that tend to phase separate are
studied including a long-range 1/r repulsive interaction. It is observed that
charge-density-wave states become stable as the strength of the 1/r term, ${\rm
V_{coul}}$, is increased. Due to this effect, the domain of stability of the
superconducting phases that appear near phase separation at ${\rm V_{coul} =
0}$ is not enlarged by a 1/r interaction as naively expected. Nevertheless,
superconductivity exists in a wide region of parameter space, even if phase
separation is suppressed. Our results have implications for some theories of
the cuprates.
