In a world where the Nash bargaining solution is operant, we consider simple two-person bargaining problems with monetary payoffs and threat point at the origin, and before the bargaining solution is applied we allow the alteration of the bargaining set by means of pre-donations of a share in one's would-be payoffs to one's opponent. Thus, a pre-bargain stage is instituted in which the bargainers may manipulate, via pre-donations, the (Nash) bargaining solution as applied in the next (bargaining) stage. We concentrate on the simple bargaining problems with triangular bargaining set and show that these are always manipulated by the luckier bargainer (with greater ideal payoff) giving a pre-donation, her best pre-donation transforming the bargaining set into one on which the Nash bargaining solution distributes payoffs in accordance with the Talmudic rule of dividing disputed property (as applied to the original simple bargaining problem whose ideal payoffs are interpreted as the bargainers' claims on a common pie of size equal to the greater of the ideal payoffs). The other bargainer always remains passive, responding to any pre-donation from his opponent by only a nil pre-donation in reverse.