Since 2000 U.S. inflation has remained both below target and silent to domestic slack and monetary interventions. A trend-cycle BVAR decomposition explores the role of imported intermediate goods in explaining the puzzling behaviour of inflation. The trend analysis shows that, starting from the `90s, despite very well-anchored expectations, slow-moving imported "cost-push" factors induced deflationary pressure keeping trend inflation below target. The cycle block provides evidence in favour of a flattening of the Phillips curve, mainly attributable to a weaker wage pass-through. The business cycle behaviour of inflation is determined by a shock originating abroad, which indeed generates the main bulk of volatility in the international prices of intermediate goods and is poorly connected to the domestic slack.