We give a detailed description of a recently completed search for a permanent electric dipole moment of199Hg.The measurement is done in an entirely new apparatus that improves the statistical sensitivity per unit time by an order of magnitude compared with the previous version of the experiment. Our measurements gived(199Hg)=−(1.06±0.49±0.40)×10−28 e cm,which we interpret as an upper limit|d(199Hg)|<2.1×10−28 e cm(95&percent; C.L.). This improves the previous limit on the199HgEDM by a factor of 4. The result sets new limits on&thgr;&vec;QCD,chromo-EDMs of the quarks, and CP violation in Supersymmetric models. We also briefly describe subsequent upgrades of the experiment which improved our sensitivity by another factor of 2. ©2001 American Institute of Physics.