The high-pressure magnetic properties of the heavy lanthanide elements Gd, Tb, Dy, Ho, Er, and Tm have been investigated using ac-magnetic susceptibility with a diamond anvil cell. It is found that the magnetic transition temperatures monotonically decrease with increasing pressure. In addition, the amplitudes of the magnetic transition signals decrease with increasing pressure, with the signals all eventually disappearing at pressures of 20 GPa. In contrast to previous studies, we see no evidence of any pressure-induced transitions from one magnetically ordered phase to another in Gd, Tb, Dy, or Ho. The transition temperatures Tcrit are all found to drop at a rate proportional to their de Gennes factor, and the values of Tcrit Tcrit (P=0) vs P Pcrit, where Pcrit is the pressure at which the magnetic transition disappears, all sit on a single phase diagram. © 2005 The American Physical Society.