This study explores the effects of anonymity on group behavior and structure. We hypothesize that there is an optimal degree of anonymity for each type of task complexity. A completely anonymous group is expected to outperform its semi-anonymous counterpart on brainstorming tasks. However, we expect the greater knowledge of team structure and the high trust and cohesion that exist in semi-anonymous groups to help these groups do better on decision making tasks. This study further examines the role of trust in encouraging information sharing and critical evaluation. We find that high levels of trust may not be optimal when it leads to groups lowering their evaluation of teammate's suggestions. In this case a certain amount of distrust may be the key to strong group performance.