Southwest Airlines will start charging $35 to check a bag for many passengers on reservations made after May 28.

Southwest Airlines ends its free checked bags policy starting May 29, implementing $35-45 fees while preserving perks for premium customers and loyalty members.

Southwest will continue to offer two free checked bags to Rapids Rewards A-List Preferred Members and customers traveling on Business Select fares. It will offer one free checked bag to A-List members and other select customers, according to a Southwest newsroom release. The airline will credit one checked bag to Rapid Rewards Credit Cardmembers.

Jefferies lifted its rating on Southwest Airlines Co. (NYSE:LUV) to Hold from Underperform after meeting with CEO Bob Jordan and CFO Tom Doxey. Analyst Sheila Kahyaoglu pointed to growing confidence in the airline company's realizable initiatives.

Southwest officials in a March announcement said the changes are "aimed to deepen and reward loyalty between Southwest and its most engaged Customers."

Southwest announced Tuesday it will start levying on its passengers a $35 fee for one checked bag, and $45 for a second. Customers that hold Business Select or Choice Extra premium tickets can check two bags for free, while its A-List and Rapid Rewards credit card holders will be allowed to check one free of charge.

Southwest Airlines is officially ending their "bags fly free" policy. The airline announced the change in March, saying at the time that the new policy would start with flights booked on Wednesday. Southwest said passengers' first checked bag will incur a fee of $35,