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Theories of sentence processing can be classified by the role that lexical heads play in first-pass parsing. In some theories, syntactic structure cannot even be built before it is licensed by a head (Abney, 1989; Prichett, 1992), whereas in other models, at the opposite extreme, only major category information in lexical items is used during the rule-based initial structure building process (Ferreira & Henderson, 1990; M itchell, 1987). In this paper, we will introduce a fully increm ental model that accounts for attachment preferences by the linear order of lexical heads in the surface structure and their thematic properties. The principle of "parameterised head attachment" and a serial variant, the SOUL mechanism, will be discussed on the basis of three on-line experim ents on NP- and PP-attachment in German verb-second and verb-final sentences.