bound by about 90-150 MeV. Moderate dependence on the KN interactions is found, provided these are constrained by the shape of $\Lambda(1405)$ and the value of the KN scattering length. However, the position of $\Lambda(1405)$ itself is not well known and this becomes the source of a large uncertainty. The effect of $ \Sigma(1385)$ on the binding energy is limited, In the states bound via $\Lambda(1405)$ it adds some 5-10 MeV contribution to the KNN binding and 10-20 MeV to KNNN binding. In this sense the suggestions of Ref. [@WYC07] are not fully supported. However, the effect of $ \Sigma(1385)$ on the space structure of deeply bound kaonic states is strong. The $ \Sigma(1385)$ is formed in peripheral regions and it absorbs a large fraction of the total K meson binding. In consequence the radii of these systems are fairly large and the nucleon densities are comparable to those met in the $^4$He nuclei.

4\) The problem of uncertainties related to the large recoil momenta entering Eq.([\[1\]]{}) is only partly removed. Large kaon momenta are hidden inside the resonant structures. In principle these may be kept under control with the help of other experiments. In practice it is not the 