In standard model-theoretic semantics, logical terms are said to be fixed in the system while nonlogical terms remain variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing them precisely amounts to. My proposal is that when a term is considered logical in a system, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea. Further, I show that under certain natural assumptions, some aradigmatic examples of nonlogical terms cannot be fixed in a standard system: they require more structure than such a system affords. We thus obtain a precondition for logical terms. I then propose a graded account of logicality: the less structure a term requires, the more logical it is. Finally, I relate this idea to invariance criteria for logical terms. Invariance criteria can be used as a tool in determining how much structure a term needs in order to be fixed. Thus, rather than settling on one criterion for logicality, I use invariance conditions as a measure for logicality.