Code readability and software complexity are important software quality metrics that impact other software metrics such as maintainability, reusability, portability and reliability. This paper presents an empirical study of the relationships between code readability and program complexity. The results are derived from an analysis of 35 Java programs that cover 23 distinct code constructs. The analysis includes six readability metrics and two complexity metrics. Our study empirically confirms the existing wisdom that readability and complexity are negatively correlated. Applying a machine learning technique, we also identify and rank those code constructs that substantially affect code readability.