  Deeply bound KNN, KNNN and KNNNN states are discussed. The effective force
exerted by the K meson on the nucleons is calculated with static nucleons. Next
the binding energies are obtained by solving the Schrodinger equation or by
variational calculations.
  The dominant attraction comes from the S-wave Lambda(1405) and an additional
contribution is due to Sigma(1385). The latter state is formed at the nuclear
peripheries and absorbs a sizable piece of the binding energy. It also
generates new branches of quasi-bound states. The lowest binding energies based
on a phenomenological KN input fall into the 40-80 MeV range for KNN, 90-150
MeV for KNNN and 120-220 MeV for K-alpha systems. The uncertainties are due to
unknown KN interactions in the distant subthreshold energy region.
