  We study two effective models developed for description of superconductors
with short-coherence length: (i) the extended Hubbard model with on-site
attraction and intersite repulsion, (ii) the model of hard-core charged bosons
on a lattice. The analysis is concentrated on the problem of phase separations
and competition between superconductivity (SS) and charge-density-wave (CDW)
orderings. The phase diagrams of the systems are shown to consist of at least
seven different states, including 3 types of phase separated (PS) states:
CDW-SS (PS1), CDW-normal (PS2) and the state of electron droplets (PS3). By
taking into account the PS states and the effects of longer-range
density-density interactions (beyond nearest neighbours) our work substantially
generalizes and modifies the conclusions of previous works concerning the
models considered.
