Solids contained in waste water are separated and dewatered by a separator comprising a cylindrical strainer basket and a rotary screw disposed in said basket. The screw terminates short of an outlet end of the basket. Waste water introduced into the separator is advanced by the screw until a solids slug is formed between a discharge end of the screw and a solids discharge formed by a cylindrical tube extending forwardly from the basket. About seventy to ninety-five percent of the slug is contained in the basket and is pressed laterally against a wall of the basket to promote the removal of water. The terminal portion of the screw tapers in order to maximize the compaction of the solids slug.