A method for a storage system to reduce data movement for snapshot copy-on-write operations, comprising: providing a live virtual volume comprising a plurality of snapshot chunks (202-1, 202-2, 202-3), each snapshot chunk of said plurality of snapshot chunks comprising a plurality of deduplication chunks (1, 2, 3, 4), wherein each one of said plurality of deduplication chunks is mapped to a disk chunk (X, Y, Z, W) on a disk; creating a snapshot of the virtual live volume without copying any of the live volume's underlying data in the disk by mapping each of a plurality of deduplication chunks (1', 2', 3', 4') of each of a plurality of snapshot chunks (204-1, 204-2, 204-3) composing said snapshot, to a respective disk chunk (X, Y, Z, W) on said disk; and in response to a host write operation to a snapshot chunk of the virtual live volume that includes a set of deduplication chunks (1, 2, 3, 4) mapped to disk chunks (X, Y, Z, W) also mapped from a snapshot, performing a snapshot copy-on-write operation using a deduplication operation by: determining for each deduplication chunk of the snapshot chunk being written by said host write operation to the virtual live volume, when data is changed in a certain deduplication chunk; and mapping the changed deduplication chunk of the snapshot chunk of the virtual live volume to a different disk chunk or to a new disk chunk; wherein a disk chunk mapped from said certain deduplication chunk of said snapshot chunk of said virtual live volume before said host write operation and mapped from said snapshot, is kept mapped from said snapshot after said host write operation; wherein a changed deduplication chunk is mapped to: a different disk chunk if its data pattern matches an existing pattern in deduplication database, a new disk chunk if its data pattern is new and therefore does not match any existing pattern in deduplication database; and wherein a snapshot chunk is the logical unit in which a snapshot layer performs copy-on-write operations when the virtual live volume is modified. providing a live virtual volume comprising a plurality of snapshot chunks (202-1, 202-2, 202-3), each snapshot chunk of said plurality of snapshot chunks comprising a plurality of deduplication chunks (1, 2, 3, 4), wherein each one of said plurality of deduplication chunks is mapped to a disk chunk (X, Y, Z, W) on a disk; creating a snapshot of the virtual live volume without copying any of the live volume's underlying data in the disk by mapping each of a plurality of deduplication chunks (1', 2', 3', 4') of each of a plurality of snapshot chunks (204-1, 204-2, 204-3) composing said snapshot, to a respective disk chunk (X, Y, Z, W) on said disk; and in response to a host write operation to a snapshot chunk of the virtual live volume that includes a set of deduplication chunks (1, 2, 3, 4) mapped to disk chunks (X, Y, Z, W) also mapped from a snapshot, performing a snapshot copy-on-write operation using a deduplication operation by: determining for each deduplication chunk of the snapshot chunk being written by said host write operation to the virtual live volume, when data is changed in a certain deduplication chunk; and mapping the changed deduplication chunk of the snapshot chunk of the virtual live volume to a different disk chunk or to a new disk chunk; determining for each deduplication chunk of the snapshot chunk being written by said host write operation to the virtual live volume, when data is changed in a certain deduplication chunk; and mapping the changed deduplication chunk of the snapshot chunk of the virtual live volume to a different disk chunk or to a new disk chunk; wherein a disk chunk mapped from said certain deduplication chunk of said snapshot chunk of said virtual live volume before said host write operation and mapped from said snapshot, is kept mapped from said snapshot after said host write operation; wherein a changed deduplication chunk is mapped to: a different disk chunk if its data pattern matches an existing pattern in deduplication database, a new disk chunk if its data pattern is new and therefore does not match any existing pattern in deduplication database; and a different disk chunk if its data pattern matches an existing pattern in deduplication database, a new disk chunk if its data pattern is new and therefore does not match any existing pattern in deduplication database; and wherein a snapshot chunk is the logical unit in which a snapshot layer performs copy-on-write operations when the virtual live volume is modified.