  In this paper we continue the program, initiated in Ref. hep-th/0112246, to
investigate an integrable noncommutative version of the sine-Gordon model. We
discuss the origin of the extra constraint which the field function has to
satisfy in order to guarantee classical integrability. We show that the system
of constraint plus dynamical equation of motion can be obtained by a suitable
reduction of a noncommutative version of 4d self-dual Yang-Mills theory. The
field equations can be derived from an action which is the sum of two WZNW
actions with cosine potentials corresponding to a complexified noncommutative
U(1) gauge group. A brief discussion of the relation with the bosonized
noncommutative Thirring model is given. In spite of integrability we show that
the S-matrix is acasual and particle production takes place.
