  In our work we consider the following problem in the context of
teleportation: an unknown pure state have to be teleported and there are two
laboratories which can perform the task. One laboratory uses a pure non
maximally entangled channel but has a capability of performing the joint
measurement on bases with a constrained degree of entanglement; the other lab
makes use of a mixed X-state channel but can perform a joint measurement on
bases with higher entanglement degrees. We compare the average teleportation
fidelity achieved in both cases, finding that the fidelity achieved with the
X-state can surpass the obtained with a pure channel, even though the X-state
is less entangled than the latter. We find the conditions under which this
effect occurs. Our results evidence that the entanglement of the joint
measurement plays a role as important as the entanglement of the channel in
order to optimize the teleportation process. We include an example showing that
the average fidelity of teleportation obtained with a Werner state channel can
be grater than that obtained with a Bell state channel.
