At a very low specific speed (VLSS), pumps normally suffer from high disk friction losses. In order to solve this issue, it can be helpful to use a different centrifugal pump design, which is not often found in the pump industry: the Pitot-tube jet pump (PTJ pump). It shows superior performance at low specific speed due to a rather unconventional working principle, described in detail in this paper. The key design feature of the PTJ pump is the (fixed) pick-up tube. Its geometry has not varied over the last decades; it is referred to in this study as “initial” or “standard” design configuration. However, optimizing the pick-up tube might lead to a considerably higher performance. Therefore, a parameterized three-dimensional (3D) computer-aided design (CAD) model is used in this study to investigate the impact of shape deformation on pump performance with the help of computational fluid dynamics (CFD). Two CFD approaches are presented and compared for this purpose: a computationally efficient approach with limited accuracy (low-fidelity method) and a more detailed, but computationally more expensive, high-fidelity approach. Using both approaches, it is possible to obtain highly efficient PTJ pumps. As a consequence, first design rules can be derived. Finally, the optimized design has been tested for various operation points, showing that the performance is favorably impacted along the complete characteristic curve.