Use of technology often has unpleasant side effects, which may include strong, negative emotional states that arise during interaction with computers. Frustration, confusion, anger, anxiety and similar emotion states can affect not only the interaction itself, but also productivity, learning, social relationships, and overall well-being. This paper suggests a new solution to this problem: Designing human-computer interaction systems to actively support users in their ability to manage and recover from negative emotional states. An interactive affect-support agent was designed and built to test the proposed solution in a situation where users were feeling frustration. The agent's text-only interaction used components of active listening, empathy, and sympathy, in an effort to support users in their ability to recover from frustration. The agent's effectiveness was evaluated against two control conditions, which were also text-based interactions: (1) users' emotions were ignored, and (2) users were able to report problems and "vent" their feelings and thoughts to the computer. Behavioral results showed that users chose to continue to interact with the system that had caused their frustration significantly longer after interacting with the affect-supporting agent, in comparison with the two controls. These results support the prediction that the computer can undo some of the negative feelings it causes by helping a user manage his or her emotional state. Implications of this solution are discussed, including possibilities for misuse or abuse, as well as potentially strong benefits when the approach is used correctly.