We consider automating negotiations over a matter that has multiple issues and each issue can take any one of the multiple possible values for that issue. We propose a rule that can be used during evaluation of contracts that reduces the number of possible bids from agents and hence increases the number of agents that could participate in the negotiation. We assume that each constraint corresponds to one evaluation criterion. The rule states that when evaluating contracts by a criterion, only contracts that satisfied previous criteria are considered. This is common practice in real life situation. That is, humans when evaluating possible options, often reduce the possibilities that have to be evaluated at each step by eliminating those that did not satisfy the previous criteria. We show how to use the rule by adapting a negotiation scenario from literature. The negotiation is between an employer and candidate employee.We also explore using the monetary values as weights for constraints of agents.