Overall, the ECB managed monetary policy quite satisfactory in the first phase of EMU. Nevertheless, this paper asks whether monetary policy could not have been improved. In the last three years, Euroland was confronted with the first external shock. Oil prices increased considerably, leading to an increase of headline inflation of over one percentage point in 2000/2001. With a specific Taylor rule one can very well understand, how the ECB sets interest rates, but it turns out that monetary policy based on the estimated Taylor reaction function was rather backward than forward-looking. While it reacted with a lag to the actions of US's Fed, it was overly cautious by targeting total HICP inflation. Here it is strongly argued and also demonstrated with model simulations that a monetary policy oriented towards "core" inflation would have resulted in a much better economic performance. The business cycle downturn could have been mitigated with no additional inflation risks.