Disseminating large files in opportunistic networks requires splitting the content into smaller pieces in order to leverage short contacts between nodes on the move. A negative consequence of content chopping is that it may generate significant overhead, as nodes have to exchange more signaling information to determine which pieces the neighbor misses. In this paper, we investigate the convenience of exchanging a burst of pieces at once at the risk of sending redundant pieces. Although achieving a good tradeoff between signaling reduction and redundant transmissions is challenging, we found out that node degree is a good indicator to determine burst size. We propose a distributed multi-content dissemination protocol with an adaptive burst dimensioning based on the device neighborhood density.We score its performance using both synthetic mobility traces and a testbed composed of real mobile devices and finely monitor the behavior of the protocol by deploying passive monitors in the target area. Our experiments show that our proposal achieves much faster dissemination than related alternatives that employ a fixed burst size. As a matter of fact, our work provides insights into the necessity of adopting adaptive strategies in practical situations involving device-to-device content dissemination.