Starting from the algorithm of asynchronous backtracking (ABT), a unifying framework for some of the asynchronous techniques has recently been suggested. Within this unifying framework, several techniques have been derived, known as the ABT family. They differ in the way they store nogoods, but they all use additional communication links between unconnected agents to detect obsolete information. A first way to remove obsolete information is to add new communication links to allow a nogood owner to determine whether this nogood is obsolete or not. The second solution consists in temporary keeping the links. A new link remains until a fixed number of messages have been exchanged through it. After that, it is removed. There is no optimal value determined for that number of messages. This article investigates different values for the number of messages, values that are either statically determined (before the run) or dynamically during the runtime. A dynamical solution for determining the number of messages necessary for maintaining a connection is proposed, the experiments show a better efficiency in comparison with the standard Yokoo variant.