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One of the issues raised by liaison concerns the lexical status of liaison consonants (LCs). LCs are generally assumed to be lexically attached to the preceding word. It has also been proposed that they are epenthetic and lexically independent, or that they belong to the following word. This issue is revisited in light of new or neglected data, notably from acquisition and phonetics. In the general case LCs are argued to be epenthetic, but in marginal cases they correspond to (fixed) initial or final consonants belonging to distinct allomorphs of the following or preceding word. The model of liaison that emerges from these different categories of LCs differs from the traditional view in several respects. First, liaison is not considered a uniform process. Second, “floating” segments are evacuated. Third, liaison appears to be driven by a constraint requiring lexical invariance, as it involves no modifications of lexical forms, and a constraint against allomorphy. This approach is characterized by the unicity, simplicity, and invariance of lexical forms. By contrast, previous analyses have viewed liaison as a simple and unified process, but they involve either numerous lexical exceptions, widespread allomorphy, or complex autosegmental representations.