Screw-spindle vacuum pump with at least three closed-off feed chambers located one behind the other along each rotor and method for operating this compressor. The chamber which is last on the delivery side is brought virtually to the compression limit pressure by means of pre-admission, shortly before it opens towards the delivery side, by supplying a pre-admission stream which is at least five times as great as the intake mass stream. A precondition, in this case, is a minimum ratio of external compression to internal compression of five.