A method of simplification of switching functions involving a very large number of ‘ don't care’ states is suggested in the present paper. First a tabular technique is suggested which generates all the prime implicants starting from the maxterm type expressions of switching functions, avoiding generation of the prime implicants formed of ‘don't care’ states only. The technique presented is simple and iterative. Next it is suggested how the knowledge of the sets of prime implicants thus obtained can be utilized for finding minimal or other irredundant sums of switching functions.