Cellular operators count on the potentials of offloading techniques to relieve their overloaded data channels. Beyond standard access point-based offloading strategies, a promising alternative is to exploit opportunistic direct communication links between mobile devices. Nevertheless, achieving efficient device- to-device offloading is challenging, as communication opportunities are, by nature, dependent on individual mobility patterns. We propose, design, and evaluate DROiD (Derivative Reinjection to Offload Data), an original method to finely control the distribution of popular contents throughout a mobile network. The idea is to use the infrastructure resources as seldom as possible. To this end, DROiD injects copies through the infrastructure only when needed: (i) at the beginning, in order to trigger the dissemination, (ii) if the evolution of the opportunistic dissemination is below some expected pace, and (iii) when the delivery delay is about to expire, in order to guarantee 100% diffusion. Our strategy is particularly effective in highly dynamic scenarios, where sudden creation and dissolution of clusters of mobile nodes prevent contents to diffuse properly.We assess the performance of DROiD by simulating a traffic information service on a realistic large-scale vehicular dataset composed of more than 10,000 nodes. DROiD substantially outperforms other offloading strategies, saving more than 50% of the infrastructure traffic even in the case of tight delivery delay constraints. DROiD allows terminal- to-terminal offloading of data with very short maximum reception delay, in the order of minutes, which is a realistic bound for cellular user acceptance.