A Coulomb lattice-gas model with a host-lattice screening mechanism is adapted to describe the ordering phenomena in alkali-metal fullerides of body-centred-cubic structure. It is assumed that the electric charge of an alkali ion residing at a tetrahedral interstitial site is completely screened by its first-neighbour molecules. The electronic energy of the ion is also taken into consideration as a charged spherical shell. By means of these assumptions an effective (short-range) pair interaction between two alkali ions is obtained. The resultant lattice-gas model is analysed by using two- and six-sublattice mean-field approximations. The thermodynamic properties are summarized in phase diagrams for different shell radii.