This paper investigates the nature of the discourse domain involved with focus sentences. The major theories of focus including Roothian Alternative Semantics are critically reviewed: Alternative Semantics takes a contradictory attitude toward the truth conditional aspect of free focus. The truth conditional differences are treated as a pragmatic inference, while they are captured by the semantic mechanism, that is, the alternative sets generated by focus constructions. In addition, the alternative sets are ad hoc since they are generated only for focus constructions. This paper attempts to show that the alternative sets introduced by foci in the framework of Alternative Semantics are neither necessary nor sufficient for an analysis of focus. It is argued that the domain sets simply provided by the model itself suffices for a proper analysis of focus constructions.