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Russia's invasion of Ukraine fuelled an energy crisis, which considerably impacted Europe given its heavy reliance on Russian natural gas imports. This study uses an ensemble of four global integrated assessment models, which are further soft-linked to two sectoral models, and explores the synergies and trade-offs among three approaches to living without Russian gas in Europe: (a) replacing with other gas imports, (b) boosting domestic energy production, and (c) reducing demand and accelerating energy efficiency. We find that substituting Russian gas from other trade partners would miss an opportunity to accelerate decarbonisation in end-use sectors while risking further fossil-fuel lock-ins, despite featuring the lowest gas price spikes and potentially reducing heating costs for end-users in the near term. Boosting domestic, primarily renewable, energy production on the other hand would instead require considerable investments, potentially burdening consumers. Energy demand reductions, however, could offer considerable space for further emissions cuts at the lowest power-sector investment costs; nonetheless, an energy efficiency-driven strategy would also risk relocation of energy-intensive industries, an aspect of increasing relevance to EU policymakers. • Three 'corner' strategies to replacing Russian natural gas in the EU are explored. • EU climate targets can still be reached in all three strategies, but costs increase. • Promoting energy efficiency or domestic renewables can boost end-use decarbonisation. • An 'energy efficiency first' response may save millions € in annual electricity costs. • Southern Europe is the most vulnerable to high electricity prices across strategies. [ABSTRACT FROM AUTHOR]