Fairness is a strong concern as shown by the robust results of dictator giving and ultimatum experiments. Efficiency, measured by the sum of individual payoffs, is another potential concern in games such as the prisoners' dilemma and public good provision games. In our experiment participants can increase efficiency by gift giving at the cost of reducing their own monetary payoff. In the one-sided treatment this is only possible for one of the two partners. The two-sided treatment allows for mutual gift giving. In both cases decisions can be conditioned on whether there is or there is not an efficiency gain by gift giving. The overall conclusion from our results is that striving for efficiency is constrained by equity concerns that are less stringent in mutual exchanges than in onesided gift-relationships.