As negotiating parties narrow the gap between them, it is often tempting to offer to “split the difference.” No matter how small that difference is, however, the normal counter-response is to offer to split the remaining difference, i.e., rejecting your 50% move and countering with 25%. A safer way to accomplish splitting the difference is to tell the mediator, “We will not make a further offer, but if the other side offers $X [= 50% of the difference between the parties] we will accept it.” This suggestion does not commit you ahead of the other side. If they choose to move less than 50%, you retain the option to do so as well.