The disclosed embodiments relate to the design of an append-only data storage system that stores sets of data blocks in extents that are located in storage devices in the system. During operation of the system, when an extent is in an open state, the system allows data blocks to be appended to the extent, and disallows operations to be performed on the extent that are incompatible with data being concurrently appended to the extent. When the extent becomes full, the system changes the extent from the open state to a closed state. Then, while the extent is in the closed state, the system disallows data blocks to be appended to the extent, and allows operations to be performed on the extent that are incompatible with data being concurrently appended to the extent.