The Process: Replacing "sub-prime" cards with "better cards"

[unusuallyconfused]

After learning a lot from you guys about the wonderful world of credit, I've learned to plan ahead. So here's my question:

Obviously you can see I have quite a few "undesirable" cards like FIRST PREMIER, APPLIED BANK (unsecured), CREDIT ONE, etc. Currently, I'm paying those on time, using them heavily and for the sake of "saving money" purposfully not keeping much of a balance with them (but I do keep a balance on all of them because I've learned these cards LOVE balances and are more inclined to reward you with CLI's to get you deeper into debt - example Credit One gave a CLI and Applied Bank even though I had balances and short history with them).

I plan on replacing the "sub-prime" cards with cards that I really want. And there's the question. If I want to go for DCU credit cards, a second USAA c/c and so fourth, should I cancel the sub-prime cards FIRST or should I apply for the cards I want first and then cancel the sub-prime cards??

Or does it matter what I do first? The logic being I MIGHT get rejected for the cards I want because I have too many credit cards so I should dump the sub-primes first. Or is the logic appy for the cards I want, hope I get them, and then dump the sub-primes because I've safely been approved for the other cards?

Keep in mind that I'm not concerned with AAoA of the accounts or effect on utilization in this scenario.

I'm in the garden till at least April 2014 - so this question applies to events that shall occur sometime then.

Thanks for all the thoughtful answers in advance!

[myjourney]

Never ever cancel any cards until you are approved for the ones you want first

[daybreakgonesXe]

+1 apply for the cards you want first! Then, when the annual fee/monthly fee is due for the subprimes, and if they refuse to waive it, close them!

Remember: before apping, have all cards report 0 except for one that has 1%-9% of your overall utility. Best of luck!