  The strength of the low energy K^- nucleus real potential has recently
received renewed attention in view of experimental evidence for the possible
existence of strongly bound K^- states. Previous fits to kaonic atom data led
to either 'shallow' or to 'deep' potentials, where only the former are in
agreement with chiral approaches but only the latter can produce strongly bound
states. Here we explore the uncertainties of the K^- nucleus optical
potentials, obtained from fits to kaonic atom data, using the functional
derivatives of the best-fit chi^2 values with respect to the potential. We find
that only the deep type of potential provides information which is applicable
to the K^- interaction in the nuclear interior.
