Q: I booked a ticket on Cathay Pacific Airways from Hong Kong to Bahrain, using my American Airlines miles to upgrade to first class. But after I made the reservation, Cathay Pacific changed its schedule, and the new aircraft offered only business class and economy class.

Cathay Pacific rebooked me in business class but offered no compensation for the lost cabin I’d paid for. I contacted the airline and was told that it is not responsible for the inconvenience, and that only American Airlines could offer compensation or a rebooking.

American Airlines told me that I was not entitled to a mileage refund for the downgrade in service, as it wasn’t American’s fault.

Bottom line: I was involuntary downgraded on a confirmed first-class award ticket and told I’m entitled to nothing in return. Can you help me?

Joe Crawford, Honolulu, Hawaii

A: I’ve always said that the travel industry is quick to take your money and slow to return it. Well, here’s a twist: Apparently, it’s quick to take your miles and slow to return them, too.

Under an airline’s contract of carriage, you are entitled to compensation for an involuntary downgrade. But that only applies to a ticket you’ve paid for with real money – not to an award ticket that, according to the airline accountants, has no value (that is, no value to the airline).

How do you refund something that has no value? The right thing to do is to credit you a portion of the miles. But when there’s more than one airline involved, things can get tricky. Who is going to make the refund – your mileage airline (American) or its codeshare partner (Cathay Pacific)?

I think you should have concentrated your efforts on American. You are a frequent flier on that airline, not on Cathay Pacific. When you discovered the downgrade you should have politely – but persistently – asked for credit.

I contacted American Airlines on your behalf and learned that the answer to your question is not simple. Apparently, when you cash in miles for a ticket, American applies all the miles to the entire ticket; it does not apportion the miles among segments of the flight.

By this reckoning, the one downgraded segment you flew, from Hong Kong to Bahrain, would not entitle you to a mileage adjustment, even if you had been bumped all the way down to economy class. The reason? You were able to fly first class for the rest of your journey.

That doesn’t mean you’re out of luck. As a gesture of goodwill, American agreed to credit your account for 15,000 miles – a more than adequate compensation for the downgrade.