A closure for a container includes a base and a peripheral wall, which may have a rim forming an upper margin of the peripheral wall and surrounding the opening of the container. The rim may have an external protrusion formed integrally with and surrounding the rim. The closure may have an overlying closure portion overlying the opening of the container when the closure is mounted on the container and a skirt formed integrally with the overlying closure portion to surround the rim when the closure is mounted to the container. The skirt includes a first portion adjacent to and surrounding an external upper end of the rim and a second portion connected to the first portion via a connection. The second portion may extend downwardly from the first portion to surround the rim below its upper end when the closure is mounted on the container.