In this paper we study three different lattice-gas models for adsorption-induced surface reconstruction in a system like H/W(001). The models are based in the symmetry properties of the local potential for a tungsten surface atom, which present four equilibrium positions where such atom can be located. The two-position, the symmetrical two-position, and the four-position models differ each other in the number and location of the equilibrium positions of both the metal and the adsorption sites. Neglecting the adsorbate-adsorbate interactions, an analytical treatment is performed which allows exact solutions for the free energy of the system in each case. We calculate the ground state, and by means of Monte Carlo simulations and finite-size scaling theory, we evaluate the critical temperature as a function of coverage, T-c(theta), when the whole set of the interactions parameters is present. The phase diagrams of the three models are analyzed and compared with the experimental findings.