We have made field measurements of methane fluxes from rice paddies, fresh water lakes, and saltwater marshes to infer estimates of the size of these sources of atmospheric methane. The rice-paddy measurements, the first of their kind, show that the principle means of methane escape is through the plants themselves as opposed to transport across the water-air interface via bubbles or molecule diffusion. Nitrogen-fertilized plants release much more methane than unfertilized plants but even these measured rates are only one fourth as large as those inferred earlier by Koyama and on which all global extrapolations have been based to date. We also compare our measured methane fluxes from lakes and marshes to similar earlier data and find that extant data and flux-measurement methods are insufficient for reliable global extrapolations.