  We study the application of various forms of the coupled cluster method to
systems with paired fermions. The novel element of the analysis is the study of
the breaking and eventual restoration of particle number in the CCM variants.
We specifically include Arponen's extended coupled cluster method, which
describes the normal Hartree-Fock-Bogoliubov mean field at lowest level of
truncation. We show that all methods converge to the exact results as we
increase the order of truncation, but that the breaking of particle number at
an intermediate level means that this convergence occurs in a surprising way.
We argue that the most straightforward form of the method seems to be the most
stable approach to implement for realistic (large number of particles) pairing
problems
