An apparatus is provided for pressing a casing or a slip-fold against an adhesive-covered back and adjacent side flanks of a book block, which is conveyed while clamped into a circulating clamp of a perfect binder with the book back projecting downward. The apparatus includes a back pressing device for pressing the casing against the adhesive-covered back and a flank pressing device for pressing the casing against the side flanks. These devices are driven synchronized with the timing of the book binder clamps for conveying the book blocks. At least the flank pressing device is assigned an individual drive unit which is connected to a control device of the perfect binder.