Methane is the second strongest anthropogenic greenhouse gas and its atmospheric burden has more than doubled since 1850. Methane concentrations stabilized in the early 2000s and began increasing again in 2007. Neither the stabilization nor the recent growth are well understood, as evidenced by multiple competing hypotheses in recent literature. Here we use a multispecies two-box model inversion to jointly constrain 36 y of methane sources and sinks, using ground-based measurements of methane, methyl chloroform, and the C13/C12 ratio in atmospheric methane (δ13CH4) from 1983 through 2015. We find that the problem, as currently formulated, is underdetermined and solutions obtained in previous work are strongly dependent on prior assumptions. Based on our analysis, the mathematically most likely explanation for the renewed growth in atmospheric methane, counterintuitively, involves a 25-Tg/y decrease in methane emissions from 2003 to 2016 that is offset by a 7% decrease in global mean hydroxyl (OH) concentrations, the primary sink for atmospheric methane, over the same period. However, we are still able to fit the observations if we assume that OH concentrations are time invariant (as much of the previous work has assumed) and we then find solutions that are largely consistent with other proposed hypotheses for the renewed growth of atmospheric methane since 2007. We conclude that the current surface observing system does not allow unambiguous attribution of the decadal trends in methane without robust constraints on OH variability, which currently rely purely on methyl chloroform data and its uncertain emissions estimates.