  Recently, a new family of observables consisting of azimuthal-angle
generalised ratios was proposed in a kinematical setup that resembles the usual
Mueller-Navelet jets but with an additional tagged jet in the central region of
rapidity. Non-tagged minijet activity between the three jets can affect
significantly the azimuthal angle orientation of the jets and is accounted for
by the introduction of two BFKL gluon Green functions. Here, we calculate the,
presumably, most relevant higher order corrections to the observables by now
convoluting the three leading-order jet vertices with two gluon Green functions
at next-to-leading logarithmic approximation. The corrections appear to be
mostly moderate giving us confidence that the recently proposed observables are
actually an excellent way to probe the BFKL dynamics at the LHC. Furthermore,
we allow for the jets to take values in different rapidity bins in various
configurations such that a comparison between our predictions and the
experimental data is a straightforward task.
