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We analyse why conventional monetary policy tightening in the euro area leads to a deterioration of output in Central‐, East and Southeastern Europe (CESEE). Our findings show that negative spillovers mainly arise through a decline in CESEE imports and exports, induced by a decrease in euro area demand. Negative spillovers are amplified through knock‐on effects through third‐countries and cannot be cushioned by favourable exchange rate movements. We also find evidence for a broad‐based retrenchment of cross‐border bank flows to the region. For the CESEE policymaker, our results indicate a limited power of exchange rate policies to buffer foreign, adverse monetary policy shocks.