In the first, shorter part of the paper I point out some problems and potential misunderstandings connected with B. Berčić’s treatment of Nozick’s sensitivity condition for knowledge. In the second part of the paper I offer the condition of modal stability or limited sensitivity as a revision of Nozickian conditions for non-accidental connection between our belief and the truth of our belief. “When it is seriously possible for you to falsely believe that p,” that is a good reason for denying that you know that p. Sensitivity within limits requires that we consider more possible worlds (all within a sphere of serious or relevant possibilities) than classical sensitivity, but not the worlds outside this sphere. The idea of modal stability com...