Drop properties have been investigated by several authors and are reviewed in the first section of the paper. Let \(B\) be a closed bounded convex set in a locally convex space \(X\). The convex hull \(D(x,B)\) of the set formed by \(x\) and \(B\) is called a drop. Modifying a definition by \textit{J. R. Giles} and \textit{D. N. Kutzarova} [Bull. Aust. Math. Soc. 43, 377-385 (1991; Zbl 0754.46010)] the author says that \(B\) has the quasi-weak drop property if for any weakly closed set \(A\) disjoint from \(B\) there exists an \(x\) in \(A\) such that \(D(x,B)\cap A=\{x\}\). For Fréchet spaces \(X\) the author proves that this property of \(B\) is equivalent to weak compactness and to the weak drop property investigated by Giles and Kutzarova. As a consequence, a Fréchet space is reflexive if and only if every closed bounded convex subset has the quasi-weak drop property.