The coupling between the bleed system and the flowfield of a downstream compressor stage is studied using two approaches. In the first approach, three-dimensional, full annulus, unsteady computations simulate the flow in a low-speed research compressor with nonuniform bleed extraction. Comparisons with experimental data show that the flow prediction in the main annulus is accurate to within 0.005 of flow coefficient and of flow angle. The computational fluid dynamics (CFD) is then used to provide a description of flow within the bleed system itself. In the second approach, a two-dimensional mean radius model, similar to that adopted by Hynes and Greitzer in the previous work on compressor stability, is used to simulate the response of the compressor to nonuniform bleed. This model is validated against experimental data for a single-stage compressor, and despite the inherent assumptions (two-dimensional flow and simplified compressor response), provides a satisfactory prediction of the flow for preliminary design purposes with orders of magnitude less computational cost than full 3D CFD. The model is then used to investigate the effect of different levels of bleed nonuniformity and of varying the axial distance between the bleed and the downstream stage. Reducing bleed nonuniformity and moving the stage away from the bleed slot are predicted to reduce the circumferential nonuniformity of the flow entering the stage.