This paper introduces two new mechanisms for provision point public goods, motivated by the design of uniform price auctions: the uniform price auction mechanism (UPA) collects an endogenously determined uniform price from everyone offering at least that price, while the uniform price cap mechanism (UPC) collects the uniform price from everyone offering at least that price, plus the full offer of everyone offering less. UPA and UPC are compared with the provision point mechanism (PPM) and the proportional rebate mechanism (PR). We use undominated perfect equilibrium and the marginal penalty associated with overcontribution to provide benchmark predictions for an experimental comparison with heterogeneous induced values, and with different provision point treatments. We find UPA generates by far the highest group and individual contributions at all provision points and values, but has the lowest provision rate; UPC elicits higher aggregate contributions than PPM and PR, and has the highest provision rate, driven by higher contributions from high-value individuals, especially at moderate provision points. This is consistent with subjects offering more in mechanisms with lower expected marginal penalty, but the effect is most significant when marginal contributions are more likely to affect provision.