  We study a simple modification of the optimized random phase approximation
(ORPA) aimed at improving the performance of the theory for interactions with a
narrow attractive well by taking into account contributions to the direct
correlation function non-linear in the interaction. The theory is applied to a
hard-core Yukawa and a square-well potential. Results for the equation of
state, the correlations, and the critical point have been obtained for
attractions of several ranges, and compared with Monte Carlo simulations. When
the attractive interaction is narrow, the modified ORPA significantly improves
over the plain one, especially with regard to the consistency between different
routes to the thermodynamics, the two-body correlation function, and the
critical temperature. However, while the spinodal curve of the modified theory
is accessible, the liquid-vapor coexistence curve is not. A possible strategy
to overcome this drawback is suggested.
