Upon closer inspection, the classical view of the synchronous relationship between tropospheric methane mixing ratio and Greenland temperature observed in ice samples reveals clearly discernable variations in the magnitude of this response during the Late Pleistocene (<50kyr BP). During the Holocene this relationship appears to decouple, indicating that other factors have modulated the methane budget in the past 10kyr BP. The delta13CH4 and deltaD-CH4 of tropospheric methane recorded in ice samples provide a useful constraint on the palaeomethane budget estimations. Anticipated changes in palaeoenvironmental conditions are recorded as changes in the isotope signals of the methane precursors, which are then translated into past global delta13CH4 and deltaD-CH4 signatures. We present the first methane budgets for the late glacial period that are constrained by dual stable isotopes. The overall isotope variations indicate that the Younger Dryas (YD) and Preindustrial Holocene have methane that is 13C- and 2H-enriched, relative to Modern. The shift is small for delta13CH4 (approx. 1 per thousand) but greater for deltaD-CH4 (approx. 9 per thousand). The YD delta13CH4-deltaD-CH4 record shows a remarkable relationship between them from 12.15 to 11.52kyr BP. The corresponding C- and H-isotope mass balances possibly indicate fluctuating emissions of thermogenic gas. This delta13CH4-deltaD-CH4 relationship breaks down during the YD-Preboreal transition. In both age cases, catastrophic releases of hydrates with Archaeal isotope signatures can be ruled out. Thermogenic clathrate releases are possible during the YD period, but so are conventional natural gas seepages.