A convex bounded set \(B\) in a locally convex sapce has the weak (quasi-weak) drop property if for each weakly sequentially closed (weakly closed) set \(A\) disjoint from \(B\) there exists \(x_0\in A\) such that \(\text{conv} \{B\cup\{x_0\}\} \cap A=\{x_0\}\). The author proves that a weakly sequentially compact convex set has the weak drop property, and a weakly compact convex set the quasi-weak drop property. The examples show that the quasi-weak drop property is weaker than the weak drop property.