Well, I've swapped the USB cables and tested the connection to the external HD using each of my imac's four USB ports. Both HDs show on the desktop every time, so I think I can safely conclude that the cable is not the issue. And despite disabling sleep mode on my energy saver approximately 4 hours ago, the "not ejected properly" warning continues to pop up in its all-too-familiar and annoying way. Any ideas about other strategies I might employ to convince my Mac that I have done nothing for which I need to be ... chastised? Thank you again, Mary Read--- Manage your account options at //www.freelists.org/list/muglo