Endocentric Structuring of Projection-free Syntax puts forward a novel theory of syntax that rigidly adheres to the principle of Minimal Computation, in which a number of traditional but extraneous stipulations such as referential indices and representational labels/projections are eliminated. It specifically articulates the overarching hypothesis that every syntactic object is composed by recursive, phase-by-phase embedding of the endocentric structure {H, alpha}, where H is a head lexical item and alpha is another syntactic object (order irrelevant). The proposed mechanism achieves both theory-internal simplicity and broad empirical coverage at the same time, advancing a radically reduced conception of endocentricty/headedness while deriving a number of empirically grounded constraints on human language.