Extensive research on human cooperation in social dilemmas has shown that individuals condition their behaviour upon the behaviour of others. However, few attempts have been made to disentangle the motivations backing conditional cooperation. We try to assess the relative importance of three motives – namely reciprocity, inequity aversion, and anchoring – in a non-linear voluntary contribution experiment. We find that, for those conditionally cooperating, both reciprocity and inequity aversion represent relevant motivational factors, but the impact of inequity aversion is stronger than that of reciprocity. In contrast, anchoring plays only a marginal role. Compared to what previously found in linear voluntary contribution games, overall we find much less conditional cooperation. In a control treatment with a less complex design, conditional cooperation is higher but still comparatively low.