  The fidelity of quantum cloning is very often limited by the accompanying
unwanted transitions. We show how the fidelity can be improved by using a
coherent field to cycle away the unwanted transitions. We demonstrate this
explicitly in the context of the model of Simon {\it et al.} [J. Mod. Opt. {\bf
47}, 233 (2000) ; Phys. Rev. Lett. {\bf 84}, 2993 (2000)]. We also investigate
the effects of the number of atoms on the quality of quantum cloning. We show
that the universality of the scheme can be maintained by choosing the cycling
field according to the input state of the qubit.
