A device for processing a spine of a book block suspended from a circulating clamp on a conveyor of a bookbinding machine includes a processing device positioned opposite the clamp and facing the spine of the book block. A tensioning device is includes a fixed support roller to act perpendicularly on one side of the clamp and an overhang of the book block, and an adjustable pressing roller to act perpendicularly on another side of the clamp and the overhang of the book block. A controlled adjusting device is connected to the adjustable pressing roller. The controlled adjusting device adjusts the adjustable pressing roller based on a thickness of the book block.