The stability of reverse domains in thin films of magnetic materials having high coerciv-ity is investigated. It is shown that domains below a critical diameter are unstable and will collapse. To minimize this minimum domain diameter it is necessary to minimize domain wall energy while maximizing the product of magnetization times coercivity, M.Hc. Since M.Hc tends to be nearly a constant near the magnetic compensation temperature, it is concluded that domain wall energy a and the product M-Hcare critical parameters for assessing the use-fulness of a material for high density thermomagnetic recording applications.