Negotiation is increasingly being conducted over computer media, such as e-mail and instant messaging, because of the potential for time savings and monetary benefits. However, these media can affect negotiators’ behaviors as they engage in what is called concession making, which is a process by which they make offers that yield benefits to their opponents. In this paper, we focus on how and why conducting negotiations via computer media can affect this process, especially when negotiators have unequal power. Our research model is based on theories from the information systems, negotiation, and social psychology literatures. Via a laboratory experiment, we find that concessions made by the first individual to make an offer (the first mover) were not typically reciprocated by his/her negotiating opponent (the second mover). Thus, in the context of computer-mediated negotiation, it appears that second movers are, among other things, more likely to violate the well-established norm of reciprocity. This can result in significant disadvantages for the first mover, independent of power differences between negotiators. In addition, we find that, contrary to face-to-face negotiations, increased power of one negotiator resulted in his/her having less influence in terms of getting larger concessions from the other negotiator. In general, these findings support the notion that computer-mediated negotiation can be significantly different than face-to-face negotiation.