  We push the limits of the direct use of partially pure entangled states to
perform quantum teleportation by presenting several protocols in many different
scenarios that achieve the optimal efficiency possible. We review and put in a
single formalism the three major strategies known to date that allow one to use
partially entangled states for direct quantum teleportation (no distillation
strategies permitted) and compare their efficiencies in real world
implementations. We show how one can improve the efficiency of many direct
teleportation protocols by combining these techniques. We then develop new
teleportation protocols employing multipartite partially entangled states. The
three techniques are also used here in order to achieve the highest efficiency
possible. Finally, we prove the upper bound for the optimal success rate for
protocols based on partially entangled Bell states and show that some of the
protocols here developed achieve such a bound.
