As the Internet continues to evolve, traditional peering agreements cannot accommodate the changing market conditions. Premium peering has emerged where access providers (APs) charge content providers (CPs) for premium services beyond best-effort connectivity. Although prioritized peering raises concerns about net neutrality, the U.S. FCC exempted peering agreements from its recent ruling, as it falls short of background in the Internet peering context. In this paper, we consider the premium peering options provided by APs and study whether CPs will choose to peer. Based on a novel choice model of complementary services, we characterize the market shares and utilities of the providers under various peering decisions and identify the value of premium peering for the CPs that fundamentally determine CPs' peering decisions. We find that high-value CPs have peer pressure when low-value CPs peer; however, low-value CPs behave oppositely. The peering decisions of the high-value and low-value CPs are substantially influenced by their baseline market shares and user stickiness, respectively, but not vice versa.