Abstract Negotiation is a very common interaction between automated agents. Many common negotiation protocols work with cardinal utilities, even though ordinal preferences, which only rank the outcomes, are easier to elicit from humans. In this work we concentrate on negotiation with ordinal preferences over a finite set of outcomes. We study an intuitive protocol for bilateral negotiation, where the two parties make offers alternately. We analyze the negotiation protocol under different settings. First, we assume that each party has full information about the other party’s preference order. We provide elegant strategies that specify a sub-game perfect equilibrium for the agents. We further show how the studied negotiation protocol almost completely implements a known bargaining rule. Finally, we analyze the no information setting. We study several solution concepts that are distribution-free, and analyze both the case where neither party knows the preference order of the other party, and the case where only one party is uninformed.