  We consider one particularly interesting class of composite gauge-invariant
operators in N=4 super Yang-Mills theory. An exceptional feature of these
operators is that in the Thermodynamic Bethe Ansatz approach the one-loop
rapidities of the constituent magnons are shown to be exact in the 't Hooft
coupling constant. This is used to propose the mirror TBA description for these
operators. The proposal is shown to pass several non-trivial checks.
