We have carried out a complete, detailed study of magnetomechanical damping on a set of annealed and deformed iron specimens. The results for macroeddy-current and microeddy-current damping are consistent with previous data on iron. The macroeddy peak gives a good indicator of achieving saturation. The microeddy damping offers a usable method for estimating domain size. The slope of damping versus amplitude in the hysteretic Rayleigh region is inversely proportional to the square of a measure of internal stress, as predicted by Smith and Birchak (SB). At higher amplitudes, in annealed and slightly deformed specimens, the damping increases more rapidly than in the Rayleigh region, a phenomenon not previously recognized, and contrary to existing models. The very long straight line in the Rayleigh region, implying a lack of any linear scale for the hysteresis, suggests that there is a fractal nature to the process. This suggestion is consistent with the SB theory. A possible model for the elementary hysteretic event is the reorientation of a quadrupole as the local stress changes sign; if this process involves a random sampling of the internal stress field, the lack of scale can be accounted for.