We present a new approach to analyzing returns distributions, the Omega function, which may be used as a natural performance measure.  Analysis based on Omega is in the spirit of the downside, lower partial moment and gain-loss literatures.  The Omega function captures all of the higher moment information in the returns distribution and also incorporates sensitivity to return levels.  We indicate how this may be applied across a broad range of problems in financial analysis and apply it to a range of hedge fund style or strategy indices.