In solar wind kinetic exospheric models the exobase level is defined as the altitude where the mean free paths of the coronal protons and electrons become larger than the density scale height. For the region above this exobase, kinetic exospheric models have been developed assuming that the charged particles of the solar wind move collisionless in the gravitational, electric, and interplanetary magnetic fields, along trajectories determined by their energy and pitch angle. In these models the exobase was usually chosen at a radial distance of ~5--10 Rs, above which the total potential energy of the protons is a monotonic decreasing function of the radial distance. Although these models were able to explain many characteristics of the solar wind, they failed to reproduce the bulk velocities observed in the fast solar wind, originating from the coronal holes, without postulating proton and electron temperatures at the exobase in clear disagreement with recent measurements obtained with the SOHO satellite. Moreover, since the number density is lower in the coronal holes than in the other regions of the solar atmosphere, the altitude of the exobase is located deeper in the corona at a radial distance ~1.1--5 Rs. At these smaller radial distances, the gravitational force is larger than the electric force acting on the protons up to a radial distance rm. Therefore the total potential energy of the protons is first attractive (increasing with altitude) and then repulsive (decreasing with altitude). We describe a new exospheric model with a nonmonotonic total potential energy for the protons and show that lowering the altitude of the exobase below the maximum of the potential energy accelerates the solar wind protons to large velocities. Since the density is lower in coronal holes and the exobase is at lower altitude, the solar wind bulk velocities predicted by our new exospheric model are enhanced to values comparable to those observed in the fast solar wind.