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This paper presents a class of methods, called constraint proposal methods, for generating Pareto-optimal solutions in two-party negotiations. In these methods joint tangents of the decision makers' value functions are searched by adjusting an artificial plane constraint. The problem of generating Pareto-optimal solutions decomposes into ordinary multiple criteria decision-making problems for the individual decision makers and into a coordination problem for an assisting mediator. Depending on the numerical iteration scheme used to solve the coordination problem, different constraint proposal methods are obtained. We analyze and illustrate the behaviour of some iteration schemes by numerical examples using both precise and imprecise answers from decision makers. An example of a method belonging to the class under study is the RAMONA method, that has been previously described from a practical point of view. We present the underlying theory for it by describing it as a constraint proposal method, and include some applications.