A method and mechanism for generating a snapshot in a computing system. On initiating a snapshot of a first storage, the content of a portion of the first storage that includes at least one block is copying to snapshot storage and a copied indication for each copied block is recording in a copy map. Responsive to any write request to a block for which no copied indication has been recorded in the copy map, the content of the block is copied to the snapshot storage, prior to writing to that block. The content of other blocks for which no copied indication has been recorded in the copy map is successively copied to the snapshot storage. A copied indication for each copied block is recorded in the copy map. The successive copying can be performed as a background task.