On bound of transfinite construction of inflationary fixed point

We consider inflationary fixed point operators which are not computable in finitely many steps. In this case we prove that for any ordinal $\alpha\leq\omega^\omega$ there exists an IFP-operator converging exactly in $\alpha$ steps. For discrete order there exists an IFP-operator which can converge exactly in $\alpha$ steps for any ordinal $\alpha$.