Choosing when to communicate is a fundamental problem in multi-agent systems. This problem becomes particularly hard when communication is constrained and each agent has different partial information about the overall situation. Although computing the exact value of communication is intractable, it has been estimated using a standard myopic assumption. However, this assumption - that communication is only possible at the present time introduces error that can lead to poor agent behavior. We examine specific situations in which the myopic approach performs poorly and demonstrate an alternate approach that relaxes the assumption to improve the performance. The results provide an effective method for value-driven communication policies in multi-agent systems.