Machine learning software can be unfair when making human-related decisions, having prejudices over certain groups of people. Existing work primarily focuses on proposing fairness metrics and presenting fairness improvement approaches. It remains unclear how key aspect of any machine learning system, such as the feature set and training data, affect fairness. This paper presents results from a comprehensive study that addresses this problem. We find that extending the feature set plays a significant role in improving fairness (with an average increase rate of 38%). Importantly, and contrary to widely-held beliefs that greater fairness often corresponds to lower accuracy, our findings reveal that extending the feature set improves both accuracy and fairness. Perhaps also surprisingly, we find that extending training data does not improve fairness. Our results suggest such data enhancement can further reduce fairness when feature sets are insufficient; an important cautionary finding for practising software engineers.