The present paper tries to link the Menzerath-Altmann law (MAL) to the Heavy Constituent Shift (HCS) phenomenon and discuss their co-effect in human natural languages. We deduce a hypothesis based on MAL and HCS and then try to empirically verify it by investigating multiple language data from Surface-Syntactic Universal Dependencies (SUD). Our results show that the hypothesis is valid across the complete set of typologically diverse languages and the co-effect of MAL and HCS appears to be a very regular universal