Southwest Airlines (LUV) said Tuesday it will start charging some customers for their first and second checked baggage who do not fall under the Rapid Rewards A-List Preferred Members, A-List Members, or clients traveling on select business class, effective around May 28.

The airline will continue to offer two checked bags without any fee to Rapid Rewards A-list Preferred members and clients traveling on business select fares, it said, adding that it will also offer one free checked bag to A-list members and other select travelers, while Rapid Rewards Credit Cardmembers will be charged for one checked luggage.

Southwest said it will also roll out a new basic fare on its lowest priced tickets bought on or after May 28.

Additionally, Southwest said that flight credits issued for tickets bought on or after May 28 will expire one year or before, depending on the type of ticket purchased.

Southwest Airlines' stock was up 6.5% in recent Tuesday premarket activity.

Price: 30.01, Change: +1.83, Percent Change: +6.49