  We investigated the dependence of the $K^- d$ scattering length on models of
$\bar{K}N$ interaction with one or two poles for $\Lambda(1405)$ resonance. The
$\bar{K}NN - \pi \Sigma N$ system is described by coupled-channel Faddeev
equations in AGS form. Our new two-body $\bar{K}N - \pi \Sigma$ potentials
reproduce all existing experimental data on $K^- p$ scattering and kaonic
hydrogen atom characteristics. New models of $\Sigma N - \Lambda N$ interaction
were also constructed. Comparison with several approximations, usually used for
scattering length calculations, was performed.
