We describe the super compressible and highly recoverable response of bucky sponges as they are struck by a heavy flat-punch striker. The bucky sponges studied here are structurally stable, self-assembled mixtures of multiwalled carbon nanotubes (MWCNTs) and carbon fibers (CFs). We engineered the microstructure of the sponges by controlling their porosity using different CF contents. Their mechanical properties and energy dissipation characteristics during impact loading are presented as a function of their composition. The inclusion of CFs improves the impact force damping by up to 50% and the specific damping capacity by up to 7% compared to bucky sponges without CFs. The sponges also exhibit significantly better stress mitigation characteristics compared to vertically aligned CNT foams of similar densities. We show that delamination occurs at the MWCNT-CF interfaces during unloading, and it arises from the heterogeneous fibrous microstructure of the bucky sponges.