The assessment of the changeability of software systems is of major concern for buyers of large systems found in fast moving domains such as telecommunications. One way of approaching this problem is to investigate the dependency between the changeability of the software and its design, with the goal of finding design properties that can be used as changeability indicators. In the realm of object oriented systems, experiments have been conducted showing that coupling between classes is such an indicator. However, class cohesion has not been quantitatively studied in respect to changeability. In this research, we set out to investigate whether cohesion is correlated with changeability. As cohesion metrics. LCC and LCOM were adopted, and for measuring changeability, a change impact model was used. The data collected on three test systems of industrial size indicate no such correlation. Manual investigation of classes supposed to be weakly cohesive showed that the metrics used do not capture all the facets of class cohesion. We conclude that cohesion metrics such as LCC and LCOM should not be used as changeability indicators.