  The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in
arXiv:1203.1913 and arXiv:1203.1617 to describe the cusp anomalous dimension
contain imaginary chemical potentials and singular boundary fugacities, which
make its systematic expansion problematic. We propose an alternative
formulation based on real chemical potentials and additional source terms. We
expand our equations to double wrapping order and find complete agreement with
the direct two-loop gauge theory computation of the cusp anomalous dimension.
