The K - optical potential in the nuclear medium is evaluated self consistently from a free-space K - N t matrix constructed within a coupled-channel chiral approach to the low-energy KN data. The chiral-model parameters are fitted to a select subset of the low-energy data plus the K - atomic data throughout the periodic table. The resulting attractive K - optical potentials are relatively 'shallow', with central depth of the real part about 55 MeV, for a fairly reasonable reproduction of the atomic data with χ 2 /N~2.2. Relatively 'deep' attractive potentials of depth about 180<space>MeV, which result in other phenomenological approaches with χ 2 /N~1.5, are ruled out within chirally motivated models. Different physical data input is required to distinguish between shallow and deep K - optical potentials. The (K - s t o p ,π) reaction could provide such a test, with exclusive rates differing by over a<space>factor of three for the two classes of potentials. Finally, forward (K - ,p) differential cross sections for the production of relatively narrow deeply bound K - nuclear states are evaluated for deep K - optical potentials, yielding values considerably lower than those estimated before.