The hitherto most abstract, and hence general, argumentation system, is the one described by Dung in a paper from 1995. This framework does not allow for joint attacks on arguments, but in a recent paper we adapted it to support such attacks, and proved that this adapted framework enjoyed the same formal properties as that of Dung. One problem posed by Dung's original framework, which was neglected for some time, is how to compute preferred extensions of the argumentation systems. However, in 2001, in a paper by Doutre and Mengin, a procedure was given for enumerating preferred extensions for these systems. In this paper we propose a method for enumerating preferred extensions of the potentially more complex systems, where joint attacks are allowed. The method is inspired by the one given by Doutre and Mengin.