Here we revisit ADOPT-ing and bring two new contributions. One contribution consists of developing variations on the algorithms keeping the improvement in length of chain of causal messages without an increase in the total number of messages. While past experiments have shown that sending more feedback is better than sending the minimal information needed for correctness, new experiments show that one should not exaggerate sending too much feedback and that the best strategy is at an intermediary point. This brings large efficiency improvements.

We also find that one of the nogood storages of ADOPTing can be removed without effects on efficiency while decreasing the space complexity by a factor given by the number of agents. We also provide a more general proof showing which types of nogood storages can be used in the inference of feedback without compromising correctness. In particular we show that all such structures can be updated by sum-inference, and from threshold messages.