A method includes storing data in a non-volatile memory that includes multiple memory blocks. At least first and second regions are defined in the non-volatile memory. A definition is made of a first over-provisioning ratio between a first logical address space and a first physical memory space of the first region, and a second over-provisioning ratio, different from the first over-provisioning ratio, between a second logical address space and a second physical memory space of the second region. Portions of the data are compacted, individually within each of the first and second regions and independently of the other region, by copying the portions from one or more source memory blocks to one or more destination memory blocks using the first and second over-provisioning ratios, respectively.