This is an announcement for the paper "Dimension reduction in $L_p$, $0<p<2$" by Gideon Schechtman. Abstract: Complementing a recent observation of Newman and Rabinovich for $p=1$ we observe here that for all $0<p<2$ any $k$ points in $L_p$ embeds with distortion $(1+\e)$ into $\ell_p^n$ where $n$ is linear in $k$ (and polynomial in $\e^{-1}$). Archive classification: math.MG math.FA Mathematics Subject Classification: 46B85 Submitted from: gideon@weizmann.ac.il The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.2148 or http://arXiv.org/abs/1110.2148