  We study the production of Mueller-Navelet jets at hadron colliders in the
Balitsky-Fadin-Kuraev-Lipatov (BFKL) framework. We show that a measurement of
the relative azimuthal angle \Delta\Phi between the jets can provide a good
testing ground for corrections due to next-leading logarithms (NLL). Besides
the well-known azimuthal decorrelation with increasing rapidity interval
\Delta\eta between the jets, we propose to also measure this effect as a
function of R=k_2/k_1, the ratio between the jets transverse momenta. Using
renormalisation-group improved NLL kernel, we obtain predictions for
d\sigma/d\Delta\eta dR d\Delta\Phi. We analyse NLL-scheme and
renormalisation-scale uncertainties, and energy-momentum conservation effects,
in order to motivate a measurement at the Tevatron and the LHC.
