Storage system(s) for storing data in physical storage in a recurring manner, method(s) of operating thereof, and corresponding computer program product(s). For example, a possible method can include: upon start of a storage recurrence, destaging dirty data which had been accommodated in the cache memory prior to the start of said storage recurrence thus giving rise to destaged data group, wherein destaging is provided with no overwriting of at least superseded data destaged before starting said storage recurrence while enabling retaining metadata indicative of location of said superseded data in the physical storage space; accommodating data obtained in said cache memory subsequent to the start of said storage recurrence while preventing said data from being destaged during said storage recurrence, thus giving rise to accommodated data group; and registering a point-in-time indicative of successful destaging of the destaged data group, thereby providing an order-preservation consistency indication corresponding to said recurrence.