In previous work on cliticization, it has been assumed that two and only two strategies are available for clitic positioning: sentential second-position cliticization (Wackernagel's Law) and cliticization to a specified lexical class, most commonly V. Moreover, it has been assumed that the host in terms of which the clitic is positioned, i.e. the structural or lexical host, must also necessarily be the phonological host. This paper shows that the structural and phonological hosts need not be the same; i.e., clitics can simultaneously attach syntactically to a structural host, while attaching independently to a different phonological host. Thus the two-strategy assumption of clitic positioning and attachment is inadequate. Instead, three independent parameters are required. These binary parameters encode two structural notions—dominance and precedence—and one phonological notion—liaison. The values of the parameters constrain possible clitics to eight types, each of which is illustrated in this paper. These parameters are encoded in the lexical subcategorization frame for clitics. It is shown that clitics are phrasal affixes. Although languages appear to differ widely in types of clitics and cliticization, this paper shows how a unitary analysis of apparently diverse clitic types is possible in terms of the three-parameter system. Languages analysed include Classical Greek, Spanish, French, Ngiyambaa, Nganhcara, and some Uto-Aztecan languages.