A system and method for providing a substantially constant-time copy operation for file system objects managed by a storage server begins by generating a snapshot of at least a portion of a data set managed by the storage server. The system then performs a copy operation in the storage server to generate a copy of the data set separate from the snapshot, on a set of block locations containing a predetermined reference value. During the copy operation to generate the copy of the data set separate from the snapshot, the system can receive from a requester a first read request directed to the copy of the data set that the copy operation is to generate. In response to the first data request, the system provides data from the snapshot to the requester by the storage server.