  We report on our NLL BFKL studies of Mueller-Navelet jets. We first perform a
complete NLL BFKL analysis supplemented by a BLM renormalization scale fixing
procedure, which is successfully compared with recent CMS data. Second, we
argue for the need of a measurement of an asymmetric jet configuration in order
to perform a valuable comparison with fixed order approaches. Third, we predict
that the energy-momentum violation is rather tiny in the NLL BFKL approach, for
an asymmetric jet configuration. Finally, we argue that the double parton
scattering contribution is negligible in the kinematics of actual CMS
measurements.
