This is an announcement for the paper "Sets of unit vectors with small pairwise sums" by Konrad J. Swanepoel. Abstract: We study the sizes of delta-additive sets of unit vectors in a d-dimensional normed space: the sum of any two vectors has norm at most delta. One-additive sets originate in finding upper bounds of vertex degrees of Steiner Minimum Trees in finite dimensional smooth normed spaces (Z. F\"uredi, J. C. Lagarias, F. Morgan, 1991). We show that the maximum size of a delta-additive set over all normed spaces of dimension d grows exponentially in d for fixed delta>2/3, stays bounded for delta<2/3, and grows linearly at the threshold delta=2/3. Furthermore, the maximum size of a 2/3-additive set in d-dimensional normed space has the sharp upper bound of d, with the single exception of spaces isometric to three-dimensional l^1 space, where there exists a 2/3-additive set of four unit vectors. Archive classification: math.MG math.FA Mathematics Subject Classification: Primary 46B20. Secondary 52A21, 52B10 Citation: Quaestiones Mathematicae 23 (2000) 383-388 Remarks: 6 pages. Old paper of 10 years ago Submitted from: konrad.swanepoel@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1006.1051 or http://arXiv.org/abs/1006.1051