  The $1s$ level shift in kaonic deuterium was calculated using Coulomb
Sturmian expansion of Faddeev equations. The convergence of the method yields
an $\sim\ 1\ eV$ accuracy for the level shifts. We used three different,
realistic, multichannel $\bar{K}N$ interactions reproducing all known
experimental two-body $\bar{K}N$ data. The different results suggest, that the
level shift should be in the range $\Delta E\sim(800\pm30)-(480\pm20){\rm i}\ \
eV$. The (almost) exact level shifts were compared with values, given by the
commonly used approximations.
