Rigid site-site molecular fluids are analysed, and a formally exact expression for the virial pressure is obtained that involves the triplet site correlation function, which may be evaluated using a superposition approximation. Numerical results for a Lennard-Jones dimer are obtained using the hypernetted chain (HNC) closure with all bridge diagrams with two field points. The bridge diagrams induce the secondary peak in the site-site distribution function that is missing in the HNC. Although the internal energy and the pressure are improved by the inclusion of bridge functions, the latter is most reliably given by the bare HNC and the compressibility route.