During a period of several days when the solar wind was relatively quiet, the magnetotail boundary near lunar distance swept back and forth past Explorer 33 as the spacecraft traveled through a distance perpendicular to the Earth-sun line of about 17 Re. The boundary crossings are remarkably well-correlated with peaks in the AE index, even though the magnitudes of the peaks are only on the order of 200 nT. Examination of the regions of multiple crossings on other Explorer 33 and 35 orbits reveals that they commonly cover large distances perpendicular to the Earth-sun line, although correlation with AE is often obscured, probably by external solar wind conditions. We conclude that a substantial fraction of the scatter in published statistical plots of boundary crossing positions can be accounted for in terms of an internal substorm-related motion with an amplitude of 5--8 Re. The data suggest that the motion takes the form of a compressional deformation wave convecting down the tail.