The paper explores the significance of a contrast between generalized phrase structure grammar (GPSG), a context-free grammar with a well structured theory of features, and head-driven phrase structure grammar (HPSG), a mechanism for increasing the power of GPSG by introducing head-wrapping and lexical rules, using examples from Mandarin Chinese. A study focusing on the discontinuous idiom chunks of possessive object (POBJ) construction produced the unexpected result that even though head-wrapping is a syntactic operation introduced to account for discontinuous constituencies, POBJ data cannot be accounted for with the Head-wrap mechanisms. The adoption of Head-wrap operations as the only explanation of discontinuous constituencies predicts that one of the disjoint sub-strings must have the head of the entire constituent on its edge. The validity of Head-wrap as the mechanism for accounting for the discontinuity of syntax is challenged by the fact that the frequency/duration adverbial splits the POBJ predicate non-adjacent to the head. The failure of grammars with head-wrapping to produce a straightforward syntactic solution to the POBJ data calls for a closer examination of non-syntactic approaches. (MSE)