Strong reciprocity explains prosocial cooperation by the presence of individuals who incur costs to help those who helped them ('strong positive reciprocity') and to punish those who wronged them ('strong negative reciprocity'). Theories of social preferences predict that in contrast to 'strong reciprocators', self-regarding people cooperate and punish only if there are sufficient future benefits. Here, we test this prediction in a two-stage design. First, participants are classified according to their disposition towards strong positive reciprocity as either dispositional conditional cooperators (DCC) or dispositional free riders (DFR). Participants then play a one-shot public goods game, either with or without punishment. As expected, DFR cooperate only when punishment is possible, whereas DCC cooperate without punishment. Surprisingly, dispositions towards strong positive reciprocity are unrelated to strong negative reciprocity: punishment by DCC and DFR is practically identical. The 'burden of cooperation' is thus carried by a larger set of individuals than previously assumed.