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This study estimates the long-term trade-off between variance of inflation and variance of output facing the European monetary authorities. When the central bank pursues inflation and output gap objectives, its choice represents the limit of optimum monetary policy. A structural VAR model is used to determine a rule for optimum monetary policy. By modifying the weighting of the stabilisation objectives for growth and inflation fluctuations, respectively, we can empirically determine a long-term trade-off between the two. Application to the European series shows that monetary policy is more effective in controlling inflation than output. There seems in particular to be an incompressible threshold below which it is impossible to reduce the output variance. Moreover, the trade-off becomes very tight when the variance of inflation drops below 1%. This result suggests that when inflation is the only concern of the central bank, the output variance can be expected to be high.