We have investigated the accuracy dependence of a single-electron pump on the confinement-potential shape of a quantum dot (QD) pump. A uniquely designed QD, which employs multiple gates to control the shape of the QD potential well, is utilized for electron pumping. It has been observed that the accuracy of the pump can be dramatically enhanced by achieving smaller QD size and greater decoupling from the electrodes, which is supported by the so-called decay-cascade model. The accuracy of the pump current is estimated, based on the decay-cascade model, to be close to 0.1 ppm for 80-pA pump current when the confinement-potential shape is optimally tuned. This is the highest reported accuracy, although it is a theoretically estimated value, among QD-based pumps measured at 4.2 K in the absence of an external magnetic field. Our numerical calculations show that the enhancement of the estimated accuracy is mainly due to the increase of the electron addition energy in the QD as well as the increase of the height and thickness of the QD potential barrier.