  We present a new and efficient method for deriving finite-size effects in
statistical physics models solvable by Bethe Ansatz. It is based on the study
of the functional that maps a function to the sum of its evaluations over the
Bethe roots. A simple and powerful constraint is derived when applying this
functional to infinitely derivable test functions with compact support, that
generalizes then to more general test functions. The method is presented in the
context of the simple spin-$1/2$ XXZ chain for which we derive the finite-size
corrections to leading eigenvalues of the Hamiltonian for any configuration of
Bethe numbers with real Bethe roots. The expected results for the central
charge and conformal dimensions are recovered.
