A key feature of diagrams is well-matchedness, referred to as iconicity in philosophy. A well-matched diagram has a structural resemblance to its semantics and is believed to be an effective representation. In this paper, we view well-matchedness as a feature of diagrams' meaning carriers -- syntactic relationships that convey meaning. Each meaning carrier may or may not structurally resemble, i.e. be well-matched to, its semantics. This paper provides the first empirical study that evaluates the impact of well-matched meaning carriers on effectiveness in Euler diagrams and linear diagrams. There are two key take-away messages: using only well-matched meaning carriers led to the best task performance and using both well-matched and non-well-matched meaning carriers in a single diagram should be approached with caution.