Advice that circular dependencies between programming artefacts should be avoided goes back to the earliest work on software design, and is well-established and rarely questioned. However, empirical studies have shown that real-world (Java) programs are riddled with circular dependencies between artefacts on different levels of abstraction and aggregation. It has been suggested that additional heuristics could be used to distinguish between bad and harmless cycles, for instances by relating them to the hierarchical structure of the packages within a program, or to violations of additional design principles. In this study, we try to explore this question further by analysing the relationship between different kinds of circular dependencies between Java classes, and their change frequency. We find that (1) the presence of cycles can have a significant impact on the change proneness of the classes near these cycles and (2) neither subtype knowledge nor the location of the cycle within the package containment tree are suitable criteria to distinguish between critical and harmless cycles.