The invention relates to a security cover designed to surround a container, the cover comprising a sleeve (1) and a security strip (2) secured to an inside face of said sleeve and including at least one zone of weakness, the security strip being shaped so that when in service it surrounds the container below a finish of the container and in the immediate proximity of said finish, the security strip thus creating a compression zone compressing the container. The invention also relates to a container covered with such a cover.