This is an announcement for the paper "Some new thin sets of integers in Harmonic Analysis" by Daniel Li, Herve Queffelec, Luis Rodriguez-Piazza. Abstract: We randomly construct various subsets $\Lambda$ of the integers which have both smallness and largeness properties. They are small since they are very close, in various meanings, to Sidon sets: the continuous functions with spectrum in $\Lambda$ have uniformly convergent series, and their Fourier coefficients are in $\ell_p$ for all $p>1$; moreover, all the Lebesgue spaces $L^q_\Lambda$ are equal for $q<+\infty$. On the other hand, they are large in the sense that they are dense in the Bohr group and that the space of the bounded functions with spectrum in $\Lambda$ is non separable. So these sets are very different from the thin sets of integers previously known. Archive classification: math.FA Mathematics Subject Classification: MSC: Primary: 42A36 ; 42A44 ; 42A55 ; 42A61 ; 43A46; Secondary: The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0912.4214 or http://arXiv.org/abs/0912.4214 or by email in unzipped form by transmitting an empty message with subject line uget 0912.4214 or in gzipped form by using subject line get 0912.4214 to: math@arXiv.org.