Rising annual fees and excessive statement credits have led to some fatigue in the premium credit-card market — but consumer demand persists.

Chase and Southwest Airlines have refreshed personal and business Rapid Rewards cards, raising annual fees while adding bag, seating and boarding perks. These changes are tied to Southwest's move to assigned seating and paid bags and are accompanied by a limited-time 100,000-point sign-up bonus for personal Rapid Rewards cards.

The new Citi Strata Elite is a very attractive travel credit card, even with its $595 annual fee, but its drawbacks might be discouraging.