Jet substructure studies play a very important role in LHC phenomenology. The vibrant research in this field has led to the development of many substructure tools, which aim to facilitate the identification of boosted-object particles decaying into jets. Efficiencies of these "taggers" have been discussed in the literature using Monte Carlo event generators. We present first analytic calculations for three commonly used substructure tools, namely jet mass distributions with trimming, pruning and the mass-drop taggers. These calculations lead to significant insight into the behaviour of the different taggers, especially in the very boosted regime. They also indicate how one can obtain variants of the above taggers that have better theoretical behaviour and that improve on signal/background discrimination.