The expressibility of bounded-arity query hierarchies resulting from the extension of first-order logic by the least fixed-point, inductive fixed-point and generalized fixed-point operators is studied. In each case, it is shown that increasing the arity of the predicate variable from k to k+1 always allows some more k-ary predicates to be expressed. Further, k-ary inductive fixed-points are shown to be more expressive than k-ary least fixed-points and k-ary generalized fixed-points are shown to be more expressive than k-ary inductive fixed-points.