A computational fluid dynamics model is used to predict the oscillatory flow through tapered cylindrical tube sections (jet pumps). The asymmetric shape of jet pumps results in a time-averaged pressure drop that can be used to suppress Gedeon streaming in closed-loop thermoacoustic devices. However, previous work has shown that flow separation in the diverging flow direction counteracts the time-averaged pressure drop. In this work, the characteristics of flow separation in jet pumps are identified and coupled with the observed jet pump performance. Furthermore, it is shown that the onset of flow separation can be shifted to larger displacement amplitudes by designs that have a smoother transition between the small opening and the tapered surface of the jet pump. These design alterations also reduce the duration of separated flow, resulting in more effective and robust jet pumps. To make the proposed jet pump designs more compact without reducing their performance, the minimum big opening radius that can be implemented before the local minor losses have an influence on the jet pump performance is investigated. To validate the numerical results, they are compared with experimental results for one of the proposed jet pump designs.