What Dale says (and thanks again, Dale!) *should* be right, but OS X seems to have some obscure bugs that prevent it from doing the right thing every time it should.

If I remove the line that Dale mentioned, the script works two or three time - but then, the next time, it launches the application, and the application complains that the disk image is not available - even though it's right there on the desktop. And then the script won't work again (I mean the application won't see the disk image again) until a reboot.

When I include the unmount AND the detach lines, the script continues to work correctly even when I run it ten times - which is the most I've tried so far.

As Dale says, the script is a bit of a CPU hog when it's unmounting and detaching, but this is probably better than waiting through the reboot that seems to be required after it fails. But maybe future versions of OS X won't require all this extra work...