  We study the efficacy of two-qubit mixed entangled states as resources for
quantum teleportation. We first consider two maximally entangled mixed states,
viz., the Werner state\cite{werner}, and a class of states introduced by Munro
{\it et al.} \cite{munro}. We show that the Werner state when used as
teleportation channel, gives rise to better average teleportation fidelity
compared to the latter class of states for any finite value of mixedness. We
then introduce a non-maximally entangled mixed state obtained as a convex
combination of a two-qubit entangled mixed state and a two-qubit separable
mixed state. It is shown that such a teleportation channel can outperform
another non-maximally entangled channed, viz., the Werner derivative for a
certain range of mixedness. Further, there exists a range of parameter values
where the former state satisfies a Bell-CHSH type inequality and still performs
better as a teleportation channel compared to the Werner derivative even though
the latter violates the inequality.
