Software development teams must be able to react rapidly to changing customer requirements. Therefore, agile software development methodologies have evolved in the last decades. Interpersonal and social skills, which are influenced by personality traits, are of fundamental importance for a successful agile software development. While the significance of the human factor is widely acknowledged, scant studies investigate the impact of personality factors on software development success and those few studies report contradictory results. Hence, we conducted interviews with eleven Scrum team members from seven different companies to investigate which personal characteristics are important for agile software development success. We use the five-factor model as a theoretical basis for our investigation, more specifically, we have applied the facets developed by Costa and McCrae. This more detailed approach enables us to give an explanation of the conflicting outcomes of prior investigations. Our study contributes to existing research by suggesting that the most important facets for single Developers are altruism, compliance, tender-mindedness, dutifulness and openness to values. The Scrum Master needs tender-mindedness, assertiveness, dutifulness, achievement striving and stability. In contrast, straightforwardness, compliance, modesty, order and assertiveness are important for the Product Owner.