Distributed video coding (DVC) systems described in the literature often make use of a feedback channel to determine the rate. However, supporting such a feedback channel in practice may be difficult, particularly considering that current approaches are unable to incorporate constraints on feedback channel usage. Therefore, in this paper we propose a system in which the number of requests per Wyner-Ziv frame can be constrained to a fixed value. Our technique involves decoder-side rate estimation, modeling of its accuracy, and finally defining the number of Wyner-Ziv bits for each of the requests allowed. The experimental results indicate that the performance loss is limited when compared to a configuration operating without constraints on the feedback channel.