Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of (1 + 1)-dimensional integrable field theories. As an example, the sine-Gordon model may be obtained by dimensional and algebraic reduction from (2 + 2)-dimensional self-dual U(2) Yang-Mills through a (2 + 1)-dimensional integrable U(2) sigma model, with some freedom in the noncommutative extension of this algebraic reduction. Relaxing the latter from U(2) --> U(1) to U(2) --> U(1) x U(1), we arrive at novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is employed to construct its multi-soliton solutions. Finally, we evaluate various tree-level amplitudes to demonstrate that our model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity. (C) 2004 Elsevier B.V. All rights reserved.