Localized electrostatic wave packets in the frequency region of lower-hybrid waves have been detected by instrumented rocket payloads and recently also by the instruments on the FREJA satellite. These waves are often associated with local density depletions, indicating that the structures can be interpreted as wave-filled cavities which are strongly elongated along the magnetic field. The basic features of the observations are discussed. Based on simple statistical arguments, we attempt to present some characteristics which have to be accommodated within an ultimate theory describing the observed wave phenomena.