This is an announcement for the paper "Banach spaces of bounded Szlenk index II" by D. Freeman, E. Odell, Th. Schlumprecht, and A. Zsak. Abstract: For every $\alpha<\omega_1$ we establish the existence of a separable Banach space whose Szlenk index is $\omega^{\alpha\omega+1}$ and which is universal for all separable Banach spaces whose Szlenk-index does not exceed $\omega^{\alpha\omega}$. In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with upper estimates. Archive classification: math.FA math.AG Mathematics Subject Classification: 46B20, 54H05 The source file(s), szlenkII_new.tex: 57543 bytes, is(are) stored in gzipped form as 0809.3626.gz with size 17kb. The corresponding postcript file has gzipped size 122kb. Submitted from: schlump@math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0809.3626 or http://arXiv.org/abs/0809.3626 or by email in unzipped form by transmitting an empty message with subject line uget 0809.3626 or in gzipped form by using subject line get 0809.3626 to: math@arXiv.org.