We use principal component analysis to reassess the link between different attributes of central bank independence and inflation performance. We suggest that coding problems may account for the fact that almost none of the attributes included in the Cukierman index has a systematic, plausible relationship with inflation. The multi-faceted Cukierman index also seems to be out-performed by a much narrower index focusing solely on policy independence. These findings point to the importance of using public choice analysis to isolate the real problem here: namely, finding specific central bank structures that effectively insulate central bankers from political pressures.