ISEE 3 plasma measurements made in the distant geomagnetic tail during rapid traverals of the current sheet from one lobe to the other show that the lobe densities on opposite sides of the current sheet often differ by a factor of ~3-10 or more. On the dawnside of the tail the north lobe plasma has the higher density when the interplanetary magnetic field (IMF) has a +By component, and the south lobe plasma has the higher density when the IMF has a -By component. The sense of this asymmetry is reversed on the duskside of the tail. Such IMF-controlled asymmetries in lobe plasma density are consistent with earlier observations made much closer to earth and can be interpreted most simply as a consequence of an ''open'' geomagnetic tail.