  We prove an analogue of Fujino and Mori's ``bounding the denominators'' in
the log canonical bundle formula (see also Prokhorov and Shokurov) for Kawamata
log terminal pairs of relative dimension one. As an application we prove that
for a klt pair $(X,\Delta)$ of Kodaira codimension one and dimension at most
three such that the coefficients of $\Delta$ are in a DCC set $\mathcal{A}$,
there is a natural number $N$ that depends only on $\mathcal{A}$ for which the
round down of $\N(K_X+\Delta)$ induces the Iitaka fibration. We also prove a
birational boundedness result for klt surfaces of general type.
