  We propose and study a method for using non-maximally entangled states to
implement probabilistically non-local gates. Unlike distillation-based
protocols, this method does not generate a maximally entangled state at
intermediate stages of the process. As a consequences, the method becomes more
efficient at a certain range of parameters. Gates of the form
$\exp[i\xi\sigma_{n_A}\sigma_{n_B}]$ with $\xi\ll1$, can be implemented with
nearly unit probability and with vanishingly small entanglement, while for the
distillation-based method the gate is produced with a vanishing success
probability. We also derive an upper bound to the optimal success probability
and show that in the small entanglement limit, the bound is tight.
