A dispensing structure, and a package with a dispensing structure, is provided with a valve. In one embodiment, the dispensing structure is a multi-piece fitment. The multi-piece fitment includes a base for mounting to the container and a valve carrier for mounting to the base. A flexible, self-sealing slit-type valve is mounted within the carrier. In another embodiment, a fitment is mounted in the opening of a thin-walled, flexible, collapsible container, and the flexible valve is mounted in the fitment. In yet another embodiment, a package includes a container having a corner wall defining an opening, and a fitment is sealingly mounted to the corner wall at the opening. A valve is disposed within the fitment. A removable and disposable cover extends from the container over the fitment and at least a portion of the corner wall to define a hermetically sealed volume around the fitment. The cover may be pulled away from the container to expose the fitment.