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They definitely will let you pay off your regular balances before you pay on a promo or the opposite.
We paid $750 on the regular balance and still have $700 12 month promo. If I wouldn't have asked I am pretty sure it would go on the promo first since they can collect interest on the other purchases.
Ofcourse my question is why would you want to pay off the promo first unless its almost expired?
If they pull that crap, I will close that card or sock drawer it faster then I can get off the phone or chat.