This paper critically reviews the development of the concept of parameter and its relation with word order. As is well known, generative grammar has developed and changed a number of models when confronted with theory internal contradictions. Though the consensus within the realm of generative grammar is for Kayne’s (1994) LCA and universal SHC hypothesis, this paper shows problems with these hypotheses, which will lead us to give up them at least for the analysis of Korean data. Consequently, we should get an alternative to LCA or maintain the word order parameter