In one embodiment, a particular node in a primary DAG receives a distributed message from distributing nodes, and from this, deterministically selects a distributing node as a distributing parent in a secondary DAG from which distributed messages are to be received. The particular node may then inform the deterministically selected distributing parent that it is being used by the particular node as its distributing parent, and if the selected distributing parent is not the particular node's primary DAG parent, then the primary DAG parent is informed that it need not send distributed messages for the particular node. In another embodiment, a distributing node continues to repeat distributed messages in response to receiving notification that it is being used as a distributing parent, and if a primary DAG parent, prevents the repeating in response to receiving a notification from all of its child nodes that it need not send distributed messages.