A storage system comprises multiple storage nodes each comprising at least one storage device. Each of the storage nodes further comprises a set of processing modules configured to communicate over one or more networks with corresponding sets of processing modules on other ones of the storage nodes. The sets of processing modules of the storage nodes each comprise at least one data module and at least one control module. The storage system is configured to assign portions of a content-based signature space of the storage system to respective ones of the data modules, and to assign portions of a logical address space of the storage system to respective ones of the control modules. The assignment of portions of the logical address space to the control modules is configured to at least partially offset an unbalanced condition between local physical storage capacities of the data modules.