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It is clear that the most effective way to limit global temperature rise and associated impacts is to reduce human emissions of greenhouse gases, including methane. However, quantification of the climate benefits of mitigation options are complicated by the contrast in the timescales at which short-lived climate pollutants, such as methane, persist in the atmosphere compared to carbon dioxide. Whereas simple metrics fail to capture the differential impacts across all timescales, sophisticated climate models that can address these temporal dynamics are often inaccessible, time-intensive, require special infrastructure, and include high unforced interannual variability that makes it difficult to analyse small changes in forcings. On the other hand, reduced-complexity climate models that use basic knowledge from observations and complex Earth system models offer an ideal compromise in that they provide quick, reliable insights into climate responses, with only limited computational infrastructure needed. They are particularly useful for simulating the response to forcings of small changes in different climate pollutants, due to the absence of internal variability. In this paper, we build on previous evaluations of the freely available and easy-to-run reduced-complexity climate model MAGICC by comparing temperature responses to historical methane emissions to those from a more complex coupled global chemistry-climate model, GFDL-CM3. While we find that the overall forcings and temperature responses are comparable between the two models, the prominent role of unforced variability in CM3 demonstrates how sophisticated models are potentially inappropriate tools for small forcing scenarios. On the other hand, we find that MAGICC can easily and rapidly provide robust data on climate responses to changes in methane emissions with clear signals unfettered by variability. We are therefore able to build confidence in using reduced-complexity climate models such as MAGICC for purposes of understanding the climate implications of methane mitigation.