A Keldysh-type theory of above-threshold detachment of electrons from negative ions is developed that includes the rescattering of the detached electron on the parent atom. The rescattering potential is the sum of the polarization potential and the static potential. The low-energy part of the spectra obtained reproduces the earlier results of Gribakin and Kuchiev. It is strongly dependent on the parity of the ground state, in contrast to the rescattering-induced high-energy part, whose shape is almost independent of the ground state as well as the rescattering potential. However, its height strongly depends on the latter, that is, on the respective ion (or atom). We relate our results to the recent experiment on photodetachment of F−[I. Yu. Kiyan and H. Helm, Phys. Rev. Lett. 90, 183001 (2003)].