Slow magnetosonic shocks are an efficient way in which magnetic energy in a collisionless plasma is converted into particle flow and thermal energy. Previous analytic and simulation studies of slow shocks have suggested that their structure consists of a damped wavetrain beginning at the shock transition and extending into the downstream region. Spacecraft observations in the solar wind and the Earth's magnetotail have found structures that resemble slow shocks except that most of them do not possess a trailing wavetrain. To resolve the conflict between theory and observations of slow shocks, we have performed new simulations which correct some of the previous results and show that depending on the sonic Mach number and the ratio of electron to ion temperature, slow shocks may or may not possess a wavetrain. ¿ American Geophysical Union 1989