This invention provides a coating composition for use on a food-contact surface of a container (e.g., a food or beverage can) that includes a polymer having one or more segments of Formula I:--O--Ar--R.sub.n--C(O)--O--R.sup.1--O--C(O)--R.sub.n--Ar--0--wherein each Ar is independently a divalent aryl group (i.e., an arylene group) or heteroarylene group; R.sup.1 is a divalent organic group; each R is independently a divalent organic group; and n is 0 or 1. Containers comprising the polymer and methods of making such containers are also provided.