In electricity distribution networks, the increasing penetration of renewable energy generation necessitates faster and more sophisticated voltage controls. Unfortunately, recent research shows that local voltage control fails in achieving the desired regulation, unless there is communication between the controllers. However, the communication infrastructure for distribution systems is less reliable and less ubiquitous compared to that for the bulk transmission system. In this paper, we design distributed voltage control that uses limited communication. That is, only neighboring buses need to communicate a few bits between each other for each control step. We investigate how these controllers can achieve the desired asymptotic behavior of the voltage regulation and we provide upper bounds on the number of bits that are needed to ensure a predefined accuracy of the regulation. Finally, we illustrate the results by numerical simulations.