This article examines the welfare impact of imperfect competition in the Medicare supplement insurance (Medigap) market. Two firms control nearly three fourths of the Medigap market, and premiums exceed claims by over 25%. I find that a low price elasticity and consumers' brand preferences lead firms to engage in substantial marketing and price above cost. Therefore, the strategic behavior of insurers facing relatively inelastic demand is critical in explaining poor market performance. I also find that insurers do not capture all of the rents in this market; rents also accrue to actors who perform marketing functions, including agents and brokers.