A storage system receives an anticipatory write command corresponding to a potential subsequent write command to be received by the storage system, wherein the anticipatory write command indicates an anticipated region of logical address space that may be written to by the potential subsequent write command. The storage system determines that physical storage is not allocated to the anticipated region of logical address space. The storage system allocates physical storage to the anticipated region of logical address space from a pool of available storage managed by the storage system. The storage system creates an association between the anticipated region of logical address space and the allocated physical storage in a virtual-to-physical mapping.