Citi issues three American Airlines co-branded credit cards (Executive, Platinum Select & CitiBusiness Select). In the past I don’t think it was possible to get the miles on these cards expedited, but reader Priya let us know that Citi now has an official policy when it comes to this. If you’re willing to pay a $35 fee, you can get the miles you’ve earned from spending (e.g not the sign up bonus expedited).

To me, a flat fee of $35 to expedite your miles based on spend seems extremely excessive. Especially when the miles don’t even post instantly and you still need to wait 2-3 days. People have had some success in getting the sign up bonus expedited in the past (it seems this is at American Airlines discretion rather than Citi as they are the ones awarding those miles), you can read about those tactics and the rules for different card issuers here.
If you’re short on miles for an award you need to book soon, I’d recommend contacting American Airlines directly to see if you can work out something with them instead first. Also you can buy American Airline miles, so if you need 1,000 or less this option will be cheaper.
Thanks to reader @Roar_Singh for this information.
