Can't authorize new computer because old one is already authorized.

If you do need to de-authorize, then ctrl-shift-D (cmd-shift-D on Mac).

BUT ... You can have up to 6 devices authorized at the same time with the same Adobe ID/account.

You may have been confused by a stupid and completely misleading ADE error message.

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Sometimes ADE gets its registration/activation confused and in a semi-authorized state.

Uninstalling and reinstalling does not help, and indeed installation can even trigger this state.

Unfortunately, it often then gives misleading error messages about what is wrong.

A common incorrect message informs you that the ID is already in use on another computer and cannot be reused.

Another is  "E_AUTH_NOT_READY"

This can often be resolved by completely removing any authorization using ctrl-shift-D to the Library screen on ADE (cmd-shift-D if on Mac).

Restart ADE, and then reauthorize with your (old) Adobe ID.

In extreme cases on the mac, the following extra step has helped some people.  Navigate to /Users//Library/Application Support/Adobe/Digital Editions and drag the activation.dat file to the trash. If you are using 10.7, see Access hidden user library files | Mac OS 10.7 Lion. http://forums.adobe.com/thread/1265248?tstart=0