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If you want to redeem BA miles, you must do so with BA -- regardless of which airline you will be flying. Some partner redemptions can be done online; others can only be done by calling the BAEC Service Center.
If you are in or near a U.S. city served by Aer Lingus and want to use your miles for a trip between the U.S. and Europe without paying high fuel surcharges, call the BAEC Service Center and try to redeem for flights on EI via Dublin or Shannon.