The exchange of arguments between agents can enable the achievement of otherwise impossible goals, for example through persuading others to act in a certain way. In such a situation, the persuading argument can be seen to have a positive utility. However, arguments can also have a negative utility - uttering the argument could reveal sensitive information, or prevent the information from being used as a bargaining chip in the future. Previous work on arguing with confidential information suggested that a simple tree based search be used to identify which arguments an agent should utter in order to maximise their utility. In this paper, we analyse the problem of which arguments an agent should reveal in more detail. Our framework is constructed on top of a bipolar argument structure, from which we instantiate bonds - subsets of arguments that lead to some specific conclusions. While the general problem of identifying the maximal utility arguments is NP-complete, we give a polynomial time algorithm for identifying the maximum utility bond in situations where bond utilities are additive.