Sure, the “Fly Three, Get One Free” promotion is the current rage, but we’re pleased to note that competition for your frequent flyer business is driving even more bonus miles your way.

American AAdvantage members can earn up to 35,000 bonus miles for flights to Japan through the end of the year. First, business and full-fare coach trips earn 5,000 bonus miles for one roundtrip, 15,000 for two roundtrips and 35,000 for three roundtrips. Discounted coach earns 2,000 bonus miles for one roundtrip, 6,000 for two roundtrips and 14,000 for three roundtrips.

Registration is required. Use promo code JPN03 when visiting http://www.aa.com online.

Not to be outdone, Delta is offering up to 15,000 SkyMiles for trips to Europe. Until Sept. 30, flights between New York/JFK and Amsterdam, Athens, Barcelona, Brussels, Frankfurt, Istanbul, Madrid, Moscow, Nice, Paris, Rome or Venice earn 15,000 bonus miles for J and D classes, 10,000 bonus miles for Y, B, M and I classes and 5,000 bonus miles for H, Q, K and L classes. S, T, and U classes of service are excluded.

Northwest WorldPerks members have slightly more geographic choices, if slightly fewer miles. A roundtrip on Northwest or KLM to Europe, Africa, the Middle East, India or Asia will earn 10,000 bonus miles in World Business class or 5,000 for full-fare coach. You’ll also earn a 30-percent Discount Travel E-Cert redeemable on a future international flight.

This offer is good for travel completed between June 1 and Sept. 15. Registration is required before Aug. 30.