Previous attempts to quantify the global source strength of CH4 from natural wetlands have resulted in a range of 90--260 Tg(CH4) yr-1. This relatively uncertain estimate significantly limits our understanding of atmospheric methane. In this study we reduce this uncertainty by simulating preindustrial CH4 with a three-dimensional chemistry-transport model. Methane mixing ratios and Δ13C-CH4, as deduced from ice cores, and estimates of other preindustrial sources and sinks, are used as constraints. This yields an average preindustrial natural wetland source strength of 163 Tg(CH4) yr-1, with an estimated ¿2&sgr; uncertainty range of 130--194 Tg(CH4) yr-1. The present natural wetland source may be ~10% smaller, owing to drainage and cultivation of wetland area since 1800 A.D. The simulated pole-to-pole concentration difference is found to be rather insensitive to the assumed relative contributions of important preindustrial sources and sinks, and therefore imposes only a limited constraint on the estimate of natural wetland emissions. In contrast, Δ13C-CH4 could provide robust constraints, but, unfortunately, at present reliable measurements are absent. Estimates of the historic development of anthropogenic CH4 sources, in combination with our model calculations, can largely explain the increase of methane mixing ratios during the nineteenth century. Results for the twentieth century indicate that these historical emission inventories underestimate anthropogenic emissions by at least 10%. Simulations of preindustrial and present-day isotopic ratios show that the growth of anthropogenic sources since 1800 A.D. may have increased Δ13C-CH4 by 3%. ¿ 2000 American Geophysical Union