  Three-qubit mixed states are used as a channel for controlled quantum
teleportation (CQT) of single-qubit states. The connection between different
channel parameters to achieve maximum controlled teleportation fidelity is
investigated. We show that for a given multipartite entanglement and mixedness,
a class of non-maximally entangled mixed $X$ states ($X-$NMEMS) achieves
optimum controlled quantum teleportation fidelity, interestingly a class of
maximally entangled mixed $X$ states ($X-$MEMS) fails to do so. This
demonstrates, for a given spectrum and mixedness, that $X-$MEMS are not
sufficient to attain optimum controlled quantum teleportation fidelity, which
is in contradiction with the traditional quantum teleportation of single
qubits. In addition, we show that biseparable $X-$NMEMS, for a certain range of
mixedness, are useful as a resource to attain high controlled quantum
teleportation fidelity, which essentially lowers the requirements of quantum
channels for CQT.
