We discuss optimal disentanglement processes of states of two two-level sys
tems that 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) t
he set in which the states of one party commute with each other, by telepor
ting the states of one party (on which the disentangling machine is acting)
through three particular types of separable channels, each of which is a m
ixture 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 mad
e separable by using a physically realizable map (V) over tilde acting on o
ne party's states, if (V) over tilde (I) = I, (V) over tilde (sigma (j)) =
lambda (j) sigma (j), where lambda (j) greater than or equal to0 (for j = 1
,2,3) and lambda (1) + lambda (2) + lambda (3) less than or equal to 1.