This paper aims at studying some of the features that characterize Federal Reserve Board Chairman Alan Greenspan’s language. After a brief assessment of the readability of the texts of his public speeches and reports, an analysis of specific linguistic elements that contribute to the complexity of his discourse is provided. Hedging devices and their blurring effect are reviewed, and, beyond them, specific lexical, syntactic and discursive choices are investigated, that help Mr Greenspan to preserve a dose of ‘fuzzy transparency’ in his pronouncements. It seems that it is precisely this varied mix that makes his discourse so peculiar and puzzling for the reader.