This is an announcement for the paper "$C^k$-smooth approximations of LUR norms" by Petr Hajek and Antonin Prochazka. Abstract: Let $X$ be a WCG Banach space admitting a $C^k$-Fr\' echet smooth norm. Then $X$ admits an equivalent norm which is simultaneously $C^1$-Fr\' echet smooth, LUR, and a uniform limit of $C^k$-Fr\' echet smooth norms. If $X=C([0,\alpha])$, where $\alpha$ is an ordinal, then the same conclusion holds true with $k=\infty$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B03, 46E15 The source file(s), LUR3-13-1-2.tex: 67805 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.3623 or http://arXiv.org/abs/0901.3623 or by email in unzipped form by transmitting an empty message with subject line uget 0901.3623 or in gzipped form by using subject line get 0901.3623 to: math@arXiv.org.