You can do what you want.*
The licence covers use use on two computers.
*I always advise people to keep the old version anyway until the are completely happy with the new.
Thank you for the quick reply, John!
This question is only partly answered. His subject line question is not fully answered. His specific variation of the question is answered though. I am still trying to find the answer to his Subject line question. If an owner of an eligible older version of an adobe product buys the upgrade version. Can you keep using the previous version and then install and use the new upgrade copy on a different computer?
The way this was answered so far, sounds like regardless of the upgrade, that a single version copy is allowed to be installed on a desktop and laptop for mobility reasons.