  We present a probabilistic cloning scheme operating independently of any
phase reference. The scheme is based solely on a phase-randomized displacement
and photon counting, omitting the need for non-classical resources and
non-linear materials. In an experimental implementation, we employ the scheme
to clone coherent states from a phase covariant alphabet and demonstrate that
the cloner is capable of outperforming the hitherto best-performing
deterministic scheme. An analysis of the covariances between the output states
shows that uncorrelated clones can be approached asymptotically. An intriguing
feature is that the trade-off between success rate and achieved fidelity can be
optimized even after the cloning procedure.
