We experimentally test different rule-based contribution mechanisms in a repeated 4-player public goods game with endowment heterogeneity and compare them to a VCM, distinguishing between a random- and an effort-based allocation of endowments. We find that endowment heterogeneities limit the efficiency gains from minimum contribution rules under random allocation. Under effort-based allocations, substantial efficiency gains relative to a VCM occur, though being largely driven by significant reductions of contributions in VCM. By apparently influencing the perception of fair burden sharing, the endowment allocation procedure crucially impacts voluntary contributions under VCM, while the rule-based mechanisms generate stable efficiency levels...