  We discuss here the best disentanglement processes of states of two two-level
systems which belong to (i) the universal set, (ii) the set in which the states
of one party lie on a single great circle of the Bloch sphere, and (iii) the
set in which the states of one party commute with each other, by teleporting
the states of one party (on which the disentangling machine is acting) through
three particular type of separable channels, each of which is a mixture of Bell
states. In the general scenario, by teleporting one party's state of an
arbitrary entangled state of two two-level parties through some mixture of Bell
states, we have shown that this entangled state can be made separable by using
a physically realizable map $\tilde{V}$, acting on one party's states, if
$\tilde{V} (I) = I, \tilde{V} ({\sigma}_j) = {\lambda}_j {\sigma}_j$, where
${\lambda}_j \ge 0$ (for $j = 1, 2, 3$), and ${\lambda}_1 + {\lambda}_2 +
{\lambda}_3 \le 1$.
