The mass of the halo nuclide (11)Li has been measured with unprecedented precision with the MISTRAL mass spectrometer at CERN's ISOLDE facility. Its resulting two-neutron separation energy, S(2n) = 378 +/- 5 keV, is 25% higher than the previously accepted value and about an order of magnitude more precise than any of the previous measurements. We also report measurement of the masses of (11)Be and (12)Be. The detailed analysis of these results and their evaluation are presented, along with a discussion concerning mass models. (C) 2009 Elsevier B.V. All rights reserved.