This is an announcement for the paper "Weakly null sequences with upper estimates" by Daniel Freeman. Abstract: We prove that if $(v_i)$ is a normalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by $(v_i)$, then there exists a uniform constant $C\geq1$ such that every normalized weakly null sequence in X has a subsequence that is C-dominated by $(v_i)$. This extends a result of Knaust and Odell, who proved this for the cases in which $(v_i)$ is the standard basis for $\ell_p$ or $c_0$. Archive classification: math.FA Mathematics Subject Classification: 46B20; 46B03, 46B10 Remarks: 21 pages The source file(s), FreemanUpEst.tex, is(are) stored in gzipped form as 0705.0218.gz with size 20kb. The corresponding postcript file has gzipped size 146kb. Submitted from: freeman@math.tamu.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0705.0218 or http://arXiv.org/abs/0705.0218 or by email in unzipped form by transmitting an empty message with subject line uget 0705.0218 or in gzipped form by using subject line get 0705.0218 to: math@arXiv.org.