The structure of a uniform simple liquid is related to that of a reference fluid with purely repulsive intermolecular forces in a self-consistently determined external reference field (ERF) phi (R). The ERF can be separated into a harshly repulsive part phi (R0) generated by the repulsive core of a reference particle fixed at the origin and a more slowly varying part phi (R1) arising from a mean field treatment of the attractive forces. We use a generalized linear response method to calculate the reference fluid structure, first determining the response to the smoother part phi (R1) of the ERF alone, followed by the response to the harshly repulsive part. Both steps can be carried out very accurately, as confirmed by computer simulations, and good agreement with the structure of the full Lennard-Jones fluid is found.