We present a new experimental approach, in which anion photodetachment spectroscopy is recorded with electrons of fixed kinetic energy. This approach circumvents some shortcomings of the zero electron kinetic energy method. Our method is based on a modified magnetic bottle photoelectron spectrometer (MBPES). A tunable laser is used to detach electrons from mass selected anions, drifting collinearly with the 40 cm MBPES drift tube. To avoid Doppler broadening, a low voltage pulse removes the velocity component of anions from the detached electrons. Spectra are recorded by collecting the wavelength dependence of electron-signal at a predetermined TOF window, corresponding to a specific electron-kinetic energy. We call this approach PEACE, denoting photoelectron action spectroscopy at constant kinetic energy. Our best resolution is 0.65 meV for 1.5 meV electrons. We present a PEACE spectrum of HgCl- together with the corresponding simulated theoretical spectrum. The method is similar in resolution and data collection rates to the slow electron velocity map imaging technique recently introduced by Neumark and co-workers.