The synthesis of optimum signals for ionospheric reflection is treated in this paper. It is shown that these optimum signals, when incident on the ionosphere, result in reflected signals which are enhanced in magnitude and compressed in duration. The optimum band-limited signals are found to have relatively complicated frequency and amplitude modulations. The reflection of linearly swept carrier pulses having gaussian envelopes that approximate the optimum signals is also considered, with the result that considerable compression is seen to occur for these signals. The ionosphere is modeled as an inhomogeneous ionized medium with a linear ionization density profile and a constant collision frequency.