We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical po
int B_2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature T_c is estimated via a constant B_2*c assumption, due to the highly non linear transformation between B_2*c and T_c. This explains the previously observed validity of the law of corresponding states. The critical density rho_c is also found to be constant when measured in units of the cubed average distance between two bonded particles (1+0.5 delta)/sigma. The possibility of describing the delta -> 0 dependence with precise functional forms provides improved acccurate estimates of the critical parameters of the adhesive hard-sphere AHS model.
