This paper addresses the problem of streaming packetized media over a lossy packet network, with sender-driven (re)transmissions and receiver acknowledgments. It extends the markovian formulation of the rate- distortion optimized (RaDiO) streaming framework in allowing the transmission schedule of a media data unit to become contingent on the acknowledgements relative to other data units. Media decoding dependencies are generally considered in state-of-the-art rate-distortion optimized scheduling algorithms. However, the set of eligible packet schedules are restricted to independent streaming policies, where the transmission strategy envisioned for a data unit at future transmission opportunities only depends on its own acknowledgment, and not on the acknowledgments potentially received for other data units. This paper questions the validity of this assumption in the design of rate-distortion optimal streaming solutions, and provides a first attempt in the formal derivation of the benefit offered by dependent policies. It considers that the scheduling of a data unit at future transmission opportunities can depend on the acknowledgments received for other data units. One of the main contributions of our paper is to propose a methodology that limits the search space of dependent policies to dependencies that are likely to bring a rate-distortion benefit, in order to solve an optimization problem that is a priori computationally intractable. Extensive simulations validate the proposed approach that focuses on relevant dependencies between streaming policies. We further show that the benefit of dependent streaming policies is actually quite marginal in practical scenarios where the gain in distortion per unit of rate decreases along the media decoding dependency path. It represents the first demonstration that the common assumption of independent streaming policies is valid in many common streaming scenarios. However, experimental results still encourage a careful investigation of dependent policies when the content is characterized by a significant increase of the benefit per transmission unit brought along the data unit dependency path.