We consider the class of linear voluntary contribution games under the general assumption of heterogeneous endowments. In this context, we generalize the Galbraith Mechanism (GM) and assess its performance relative to a fixed equal sharing allocation in both theory and experiments. Three main empirical results emerge. First, the GM raises average contributions significantly above those under an equal-shares allocation. Second, the GM simultaneously reduces income inequality as it improves efficiency. Third, a player's contribution and allocation behavior is sensitive to her position in the endowment distribution. In all their decision-making, agents consistently place greater emphasis on absolute contribution levels when they are rich, and on contribution ratios (contributions relative to endowments) when they are poor.