With a high-resolution (~20 keV full width maximum (FWHM) electron spectrometer providing contiguous energy coverage from 68 to 1120 keV, a new study has been made of the previously discovered peaks in the energy spectra of electrons precipitating from the inner radiation belt. The measurements were performed from the low-altitude polar orbiting satellite P78-1. In some cases the spectral peaks that decrease in energy with increasing L shells on a satellite pass are extremely narrow, being of the order of 20 keV wide after the instrument resolution is unfolded. Such narrow widths require that the bandwidth of the responsible waves be less than ~1 kHz if the electron peaks result from first-order cyclotron resonance. A significant fraction of the interactions with nearly monochromatic waves must also take place within a narrow range of latitudes ¿5¿ if near the equator, or an even narrower interval if off the equator. The peak energy values and the behavior with L shell generally consistent with cyclotron resonance near the equator involving nearly monochromatic waves in the frequency range 10--20 kHz radiating over the interval 1.5≲L≲1.85, but significant deviations from this simple pattern are observed. The energy spectra sometimes contain additional higher-energy peaks with similar L dependences and with comparable widths, but in some cases the peaks are much broader. Peak energies of the dual set on a given orbit do not generally correspond exactly to first and second harmonic resonances with waves of the frequency, and it is concluded that another group of narrow waves may be involved.