Abstract: A binding machine is operable to hyper-deflect the rings of a binding element against non-planar surfaces to achieve an advantageously forward presentation of free ends of the rings for ergonomic and convenient insertion of a perforated stack of sheets. An embodiment of the binding machine has a base, a plurality of stationary hooks fixed to the base, and a comb member which is pivotally mounted to the base. The comb member may be fixed to a shroud which is mounted to effect the pivotal movement of the comb member. Additionally, this shroud may be axially shifted. When the binding element is supported against the comb member, the axial and pivotal motions of shroud respectively cause (1) engaging of rings of the binding element with the stationary hooks and (2) uncurling deflection of the rings.