There are some well known indices of knots that give rise to classical knot invariants when minimized for a knot type. By classical knot invariants I mean the minimal number of crossing points, bridge number, braid index, genus and unknotting number. Considering these indices when restricting the minimum over holonomic knots, some of the minima stay the same while others differ. This supplies us with a new set of knot invariants: the holonomic counterparts of the classical knot invariants.