Narrow-band Electrostatic Noise (NEN) is a common occurrence in the Earth's distant magnetotail. NEN is observed in a frequency range (100--316 Hz) that falls roughly between the electron and ion plasma frequencies. This mode may result from holes in the electron distribution function associated with slow shocks. An instability that is associated with this mode is studied using numerical simulations. The growth of the instability depends on the size and shape of the hole. The hole mode can also be driven unstable by either an anisotropy in the electron distribution function or an ion beam. In all these cases the instability saturates at a low level and only a fraction of the available free energy is released. ¿ American Geophysical Union 1993