Human population and economic growth are accelerating the demand for plant biomass to provide food, fuel, and fiber. The annual increment of biomass to meet these needs is quantified as net primary production (NPP). Here we show that an underlying assumption in some current models may lead to underestimates of the potential production from managed landscapes, particularly of bioenergy crops that have low nitrogen requirements. Using a simple light-use efficiency model and the theoretical maximum efficiency with which plant canopies convert solar radiation to biomass, we provide an upper-envelope NPP unconstrained by resource limitations. This theoretical maximum NPP approached 200 tC ha(-1) yr(-1) at point locations, roughly 2 orders of magnitude higher than most current managed or natural ecosystems. Recalculating the upper envelope estimate of NPP limited by available water reduced it by half or more in 91% of the land area globally. While the high conversion efficiencies observed in some extant plants indicate great potential to increase crop yields without changes to the basic mechanism of photosynthesis, particularly for crops with low nitrogen requirements, realizing such high yields will require improvements in water use efficiency.