Aspect-oriented refactoring is a promising technique for improving modularity and reducing complexity of existing software systems through encapsulating crosscutting concerns. As complexity of a system is often linked to the degree to which its components are connected, we investigate in this paper the impact of such refactoring activities on component relationships. We analyze two aspect-refactoring projects to determine circumstances when such activities are effective at reducing component relationships and when they are not. We measure two kinds of relationships between components, use and clone relations. We compare how these metrics changed between the original and the refactored system. Our findings indicate that aspect-oriented refactoring is successful in improving the modularity and complexity of the base code. However, we obtain mixed results when aspects are accounted for. Based on these results, we also discuss constraints to the technology as well as other design considerations that may limit the effectiveness of aspect-oriented refactoring on actual systems.