Summary: This paper develops a fuzzy constraint based model for bilateral multi-issue negotiation in trading environments. In particular, we are concerned with the principled negotiation approach in which agents seek to strike a fair deal for both parties, but which, nevertheless, maximises their own payoff. Thus, there are elements of both competition and cooperation in the negotiation (hence semi-competitive environments). One of the key intuitions of the approach is that there is often more than one option that can satisfy the interests of both parties. So, if the opponent cannot accept an offer then the proponent should endeavour to find an alternative that is equally acceptable to it, but more acceptable to the opponent. That is, the agent should make a trade-off. Only if such a trade-off is not possible should the agent make a concession. Against this background, our model ensures the agents reach a deal that is fair (Pareto-optimal) for both parties if such a solution exists. Moreover, this is achieved by minimising the amount of private information that is revealed. The model uses prioritised fuzzy constraints to represent trade-offs between the different possible values of the negotiation issues and to indicate how concessions should be made when they are necessary. Also by using constraints to express negotiation proposals, the model can cover the negotiation space more efficiently since each exchange covers a region rather than a single point (which is what most existing models deal with). In addition, by incorporating the notion of a reward into our negotiation model, the agents can sometimes reach agreements that would not otherwise be possible.