Dislocation-based deformation in crystalline solids is almost always plastic. Here we show that polycrystalline samples of Ti3SiC2 loaded cyclically at room temperature, in compression, to stresses up to 1 GPa, fully recover on the removal of the load, while dissipating about 25% (0.7 MJ m(-3)) of the mechanical energy. The stress-strain curves outline fully reversible, rate-independent, closed hysteresis loops that are strongly influenced by grain size, with the energy dissipated being significantly larger in the coarse-grained material. At temperatures greater than 1,000 degreesC, the loops are open, the response is strain-rate dependent, and cyclic hardening is observed. This hitherto unreported phenomenon is attributed to the reversible formation and annihilation of incipient kink bands at room-temperature deformation. At higher temperatures, the incipient kink bands dissociate and coalesce to form regular irreversible kink bands. The loss factor for Ti3SiC2 is higher than most woods, and comparable to polypropylene and nylon. The technological implications of having a stiff, lightweight machinable ceramic that can dissipate up to 25% of the mechanical energy per cycle are discussed.