We discuss three cases of morphological complexity in order to show the relevance of Strict Asymmetry Theory for morphological analysis. The first case is overt/covert right periphery, the second case is overt/covert left periphery and the last case is mirror effect. We present an implementation of the theory for the argument structure analysis of complex morphological objects. We consider some consequences of our proposal for the properties of the interface between Morphological Form and its interpretation by the Conceptual-Intentional system. We discuss some consequences for information processing.