Southwest Airlines said Tuesday it will start charging most passengers for checked baggage, ending a longtime free-luggage policy that the company had touted as an important differentiator as recently as last fall. The new policy, which follows other quirks recently discarded by the idiosyncratic airline, applies to flights booked starting May 28.

Customers with the highest loyalty status will be spared from the fee, but others will have to pay for checked bags for flights booked from May 28.