This is an announcement for the paper "Small ball probability estimates in terms of width" by Rafal Latal and Krzysztof Oleszkiewicz. Abstract: A certain inequality conjectured by Vershynin is studied. It is proved that for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK) \leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false. Archive classification: Probability; Functional Analysis Mathematics Subject Classification: 60G15, 60E15 Remarks: 10 pages The source file(s), , is(are) stored in gzipped form as with size . The corresponding postcript file has gzipped size . Submitted from: rlatala@mimuw.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.PR/0501268 or http://arXiv.org/abs/math.PR/0501268 or by email in unzipped form by transmitting an empty message with subject line uget 0501268 or in gzipped form by using subject line get 0501268 to: math@arXiv.org.