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, Vcoul, is increased. Due to this effect, the domain of stability of the
superconducting phases that appear near phase separation at Vcoul=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.Comment: 11 pages, 9 postscript figures are appende