Summary: Given a simple graph \(G\) and vertices \(u, v \in V(G)\), let \(N_G (u)\) and \(N_G (v)\) denote the neighborhoods in \(G\) of \(u\) and \(v\) respectively. The compression of \(G\) from \(u\) to \(v\) produces a new graph \(G_{u \to v}\) by, for each \(x \in N_G (u) - N_G (v) - \{v\}\), removing edges from \(G\) of the form \(ux\) and replacing them with corresponding edges of the form \(vx\). A. Kelmans [“Operations on graphs increasing some graph parameters”, Preprint, arXiv:1109.4622], and independently A. Satyanarayana et al. [Networks 22, No. 2, 209–216 (1992; Zbl 0756.90038)], showed that for any graph \(G\) and any \(u, v \in V (G)\), compression from \(u\) to \(v\) could not increase, and typically decreased, both the number of spanning trees and the all-terminal reliability of \(G\). Both the number of spanning trees and all-terminal reliability are vulnerability parameters, i.e., measures of the strength of a network. We show that a number of other prominent vulnerability parameters – including vertex connectivity, toughness, scattering number, edge connectivity, edge toughness, and binding number – are affected by compression in the same way as number of spanning trees and all-terminal reliability. As a consequence, as with the number of spanning trees and the all-terminal reliability, threshold graphs are extremal graphs for all of the vulnerability parameters considered.