This is an announcement for the paper "A conjecture of Godefroy concerning James' theorem" by Hermann Pfitzner. Abstract: In this note we look at the interdependences between James' theorem and the boundary problem. To do so we show a variant of James' sup-theorem for C(K)-spaces conjectured by Godefroy: in order to know that a bounded weakly closed subset of a C(K)- space is weakly compact it is enough to test the sup-attainment only for measures with countable support. Archive classification: math.FA Remarks: to appear in Quarterly Journal of Math. Submitted from: Hermann.Pfitzner@univ-orleans.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1201.5471 or http://arXiv.org/abs/1201.5471