A type of ‘non-traditional constituents’ motivates an extended class of Combinatory Categorial Grammars (CCG), CCGs with Generalized Type-Raised Categories (CCG-GTRC) involving variables. Although the class of standard CCGs is proved to be equivalent to Linear Indexed Grammars and Tree Adjoining Grammars, use of variables can increase the power beyond these grammars. In order to establish a desired context with respect to computational complexity, this paper shows that there is a subclass of CCG-GTRC which is still weekly equivalent to the standard CCGs. The idea behind the proof is that the behavior of GTRCs can be simulated by appropriately setting the lexicon of a standard CCG.