The use of Named Data Networking (NDN) for distributed multi-user applications, e.g. group messaging and file sharing, requires NDN synchronization protocols to maintain the same shared dataset (and its updates) among all nodes. ChronoSync, RoundSync, and PartialSync are some proposals to address this issue. Here we focus on the state-of-the-art protocol RoundSync: we study its core features, that permit participating nodes to detect, propagate, and reconcile all changes. Particular attention is given to the case of multiple changes per round. We then propose an improved variant, iRoundSync, that exchanges fewer messages in the multiple-change case and is more resilient to packet losses. We quantify the performance gain of iRoundSync on a simple topology.