A recent theoretical study has proved that the MUMCUT testing strategy (1) guarantees to detect seven types of fault in Boolean specifications in irredundant disjunctive normal form, and (2) requires only a subset of the test sets that satisfy the previously proposed MAX-A and MAX-B strategies, which can detect the same types of fault. This paper complements previous work by investigating various methods for the automatic generation of test cases to satisfy the MUMCUT strategy. We evaluate these methods by using several sets of Boolean expressions, including those derived from real airborne software systems. Our results indicate that the greedy CUN and UCN methods are clearly better than others in consistently producing significantly smaller test sets, whose sizes exhibit linear correlation with the length of the Boolean expressions in irredundant disjunctive normal form. This study provides empirical evidences that the MUMCUT strategy is indeed cost-effective for detecting the faults considered in this paper.