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We investigate remote state preparation (RSP) via a non-maximally entangled channel for three cases: a general qubit; a special ensemble of qubits (qubit states on the equator of the Bloch sphere); and an asymptotic limit of N copies ofa general state. The results show that the classical communication cost of RSP for the two latter cases can be less than that of teleportation, but for the first case, in a restricted setting, the classical communication cost is equal to that of teleportation. Whether or not this is the case for a more general setting is still an open question.