Conceptual schemata each representing some component of a system in the making, can be integrated in a variety of ways. Herein, we explore some fundamental notions of this. More particularly, we investigate some ways in which integration through correspondence assertions affects the interrelationship of two component schemata. One of the consequences of combining schemata is the appearance of events, for the united schema, that allow spurious transitions between models, transitions that would not have been possible in one of the original schemata. Much previous work has focussed on dominance with regard to preservation of information capacity as a primary integration criterion. However, even though it is desirable that the information capacity of a combined schema dominate one or both of its constituent schemata, we here discuss some aspects of why domination based on information capacity is insufficient for the integration to be semantically satisfactory.