1. A method for use in a computer system comprising at least one mapping layer that makes available a plurality of storage objects, and a storage system that stores data in each of the plurality of storage objects in one or more data blocks, the method comprising: reducing space usage on the storage system, using a redundant data elimination tool, of at least some redundant data by sharing at least one of the data blocks among multiple storage objects; generating information about the at least one of the data blocks shared among multiple storage objects, wherein the information identifies the storage objects that include shared data blocks; assigning to the plurality of storage objects a scanning priority based at least in part on the information about the at least one of the data blocks shared among multiple storage objects, wherein a higher scanning priority is assigned for storage objects having redundant data blocks shared among multiple storage objects over storage objects that do not include a shared data block; and performing, using at least one scanning tool, at least one scanning operation on at least some of the plurality of storage objects wherein ones of the storage objects having a higher scanning priority are scanned prior to ones of the objects having a lower scanning priority.