A rotary vacuum pump includes a first set of pumping stages having rotor discs with a first diameter and a second set of pumping stages having rotor discs with a second different diameter and further comprising an intermediate pumping stage that is particularly adapted for matching the change in the diameter of the pump rotor discs. According to the invention, the intermediate pumping stage comprises a rotor disc having an outer portion in the radial direction that is axially tapered from its inner diameter to its outer diameter and a corresponding stator stage including a spacer ring that is axially tapered from its periphery toward its center.