In this thesis I set out to test three hypotheses about the organization of the Grammar; (1) That the grammar can be given a declarative interpretation, and thus no extrinsic ordering or rules is available, and that syntactic structures have a compositional semantics; (2) That all transparent concatenation results from operations of the rules of syntax; and (3) That all syntactic projections must be phonetically visible. Further, I have assumed that the relationship between the lexicon and syntactic representations is monotonic. In testing these hypotheses I develop an underspecified tree representation for lexical entries which allows lexical information to be organized in a manner which is immediately interpretable by the syntax. These lexical trees, through the formal processes of unification and tree adjunction and the operation of X-bar, yield D-structure. I propose a parametrization of case-assigning ability into the distribution of the features [+ /-NECESSARY] and [+ /-UNIQUE] and use this to derive the Extended Projection Principle (for English) and to account for agreement in Labrador Inuttus. This move forces me to arrive at a new treatment of passive in English, however, as verbs in English have the case-assigning matrix [-NECESSARY,UNIQUE] (i.e., are profligate case-assigners). The analysis of passive proposed subsumes passive to other focus rules such as topicalization, by assuming that the passive morpheme -en heads a syntactic projection and assigns the sentential theta-role TOPIC to its external argument position. Topicalization in general is also considered, and proposals made concerning the syntactic structure of topicalized sentences in both Topic Prominent and Subject Prominent Languages. In considering a theta-theoretical analysis of passive, I further propose that animacy effects are properly considered as syntactic, and are best considered as part of the information contained in theta-role assignment. Specifier positions are then considered, and the dichotomy between the characteristics of D-structure selected and un-selected specifiers is discussed. This consideration leads me to propose a revival of the Raising-to-Object Analysis, with the embedded subject raising to [SPEC, VP], from this, the parallel is drawn with passive, and the possibility of NP-movement to [SPEC,IP]. [SPEC,VP] is then considered as a similar position to [SPEC,IP] with respect to the possibility of NP-movement. Different types of relative clauses cross-linguistically are examined, and the PF-Licensing Principle is shown to make desirable predictions about the structure of the so-called headless relatives. Data from Piapoco is considered in some detail, and the PFLP is shown to derive certain attractive tree structure. Agreement in Piapoco is considered, and a feature percolation through SPEC-head coindexing is shown to give the effect of morpheme harmony on certain verbal incorporation structures. The prohibition against invisible syntactic projections and general considerations of the relationship between heads and their complements in the lexicon leads me to propose a redefinition of barrier, such that any head which selects in some way its complement L-marks that complement and thus voids its barrierhood. In this case, then barriers only arise relativized by position, i.e., specifier position and adjuncts (not sisters to lexical heads). If this definition of barrier is adopted, then Zero Subjacency holds and no counting of barriers is necessary. An extension to the X-bar schema is proposed which underlies equative or predicative constructions. Finally, the hypotheses of this thesis are tested in some detail in analyses of Labrador Inuttus and Lakhota. These analyses highlight the difference between agreement and pronominal incorporation, and the typological difference between languages with and without grammatical function changing rules and overt case marking.