Gossip protocols are a fast and effective strategy for computing a wide class of aggregate functions involving coordination of large sets of nodes. The monotonic nature of gossip protocols, however, mean that they can typically only adjust their estimate in one direction unless restarted, which disrupts the values being returned. We propose to improve the dynamical performance of gossip by running multiple replicates of a gossip algorithm, overlapping in time. We find that this approach can significantly reduce the error of aggregate function estimates compared to both typical gossip implementations and tree-based estimation functions.