The ice core record reveals large variations in the concentration of atmospheric methane, [CH4], over the last 800 kyr. Amongst the most striking natural features are the large, rapid rises in [CH4], of 100–200 ppbv, on timescales of less than 100 years, at the beginning of Dansgaard-Oeschger (D-O) events during the last glacial period (21–110 kyr before present). Despite the potential insight they could offer into the likelihood of future rapid rises in [CH4], the relative roles of changes in methane sources and sinks during D-O events have been little explored. Here, we use a global atmospheric chemistry-transport model to explore—for the first time, in a process-based fashion—controls on the oxidizing capacity during an idealized D-O event that features a characteristically rapid rise in [CH4]. We find that the two controls previously identified in the literature as having had significant (though opposing) influences on the oxidizing capacity between glacial and interglacial periods—changes in air temperature and emissions of non-methane volatile organic compounds from vegetation—offset one another between idealized Heinrich stadial and Greenland interstadial states. The result is, the net change in oxidizing capacity is very small, implying the rapid rises in [CH4] at the beginning of D-O events were almost entirely source-driven. This poses a challenge to earth-system models—to generate a sufficiently large increase in methane emissions in response to a simulated D-O event, via a more realistic freshwater forcing impacting the strength of the Atlantic meridional overturning circulation or, possibly, other climate-change mechanisms.