The authors have investigated a double differentially pumped supersonic secondary beam, primarily designed for helium and neon. The performance for helium, neon, argon, and krypton can be described in terms of the virtual source distribution and the attenuation by collisions with residual gas atoms in the differential stage and in the expansion chamber. Both theoretical insight and experimental result show that with differential pumping it is possible to produce a compact secondary beam with very low pumping speed at both the expansion chamber ( approximately 1000 l/s) and the differential stage ( approximately 10 l/s). The collimator in the differential stage has mainly a (positive) geometrical effect, resulting in narrow beam profiles at the scattering centre without far wings. The virtual source distribution and the center line intensity are only slightly affected by the collimator. The model can be used in the design phase of a secondary beam to predict the performance of the resulting supersonic beam.