The properties of bone tissue with very high or very low mineral levels attract attention because they allow researchers to comprehend more fully the mechanics, interaction and effects of mineral on collagen through a greater range of compositions than that found in the “ordinary”. The bone tissue of the rostrum of the whale Mesoplodon densirostris is the densest bone known. We examined the composition, static and fatigue strength, hardness and toughness of this tissue and compared them to those of other less mineralised analogues. The rostrum bone has remarkably little organic matter and retains very little water in its native state, but its basic mineral stoichiometry is very similar to that of other bones. We present here updated versions of the microhardness vs. modulus and microhardness vs. mineral fraction relationships, which thanks to the rostrum have been produced for a considerably wider range than in the past. We found the rostrum to be extremely brittle with a toughness ratio in two perpendicular directions (along and across its length) similar to that of tissue of other “ordinary” long bones and we discuss the possible significance of our findings.