A secure container cover for restricting access to an opening of a container comprising: an integrally molded body including an annular structure and a side wall, the annular structure including a central void defined by an intermediate perimeter, a graspable loop integrally formed with the annular structure being configured to reside within the central void, a first tear initiation point being formed at a first location where the graspable loop joins the annular structure, a first thin section extending from the first tear initiation point to a bottom edge of the side wall, the first thin section being defined by a first channel formed in the body of the secure container cover, a second tear initiation point being formed at a second location different from the first location where the graspable loop joins the annular structure, a second thin section extending from the second tear initiation point to a tear termination point on the side wall, the second thin section being defined by a second channel formed in the body of the secure container cover, the graspable loop being detachably connected to the annular structure at a bridging section, the bridging section being configured to break when an upward biasing force is applied to the graspable loop, and the side wall being configured to separate along the first thin section and the second thin section when the graspable loop is pulled away from the body of the secure container cover, characterized in that: the tear termination point is a protrusion in a tear direction and the protrusion is formed on the side wall adjacent to the bottom edge of the side wall, and the protrusion is configured as a tear barrier that prevents further separation of the side wall along the second thin section. an integrally molded body including an annular structure and a side wall, the annular structure including a central void defined by an intermediate perimeter, a graspable loop integrally formed with the annular structure being configured to reside within the central void, a first tear initiation point being formed at a first location where the graspable loop joins the annular structure, a first thin section extending from the first tear initiation point to a bottom edge of the side wall, the first thin section being defined by a first channel formed in the body of the secure container cover, a second tear initiation point being formed at a second location different from the first location where the graspable loop joins the annular structure, a second thin section extending from the second tear initiation point to a tear termination point on the side wall, the second thin section being defined by a second channel formed in the body of the secure container cover, the graspable loop being detachably connected to the annular structure at a bridging section, the bridging section being configured to break when an upward biasing force is applied to the graspable loop, and the side wall being configured to separate along the first thin section and the second thin section when the graspable loop is pulled away from the body of the secure container cover, characterized in that: the tear termination point is a protrusion in a tear direction and the protrusion is formed on the side wall adjacent to the bottom edge of the side wall, and the protrusion is configured as a tear barrier that prevents further separation of the side wall along the second thin section. the tear termination point is a protrusion in a tear direction and the protrusion is formed on the side wall adjacent to the bottom edge of the side wall, and the protrusion is configured as a tear barrier that prevents further separation of the side wall along the second thin section.