We study the decorrelation in azimuthal angle of Mueller-Navelet jets at hadron colliders within the BFKL formalism. We introduce NLO terms in the evolution kernel and present a collinearly-improved version of it for all conformal spins. We show how this further resummation has good convergence properties and is closer to the Tevatron data than a simple LO treatment. However, we are still far from a good fit. We offer estimates of these decorrelations for larger rapidity differences which should favor the onset of BFKL effects and encourage experimental studies of this observable at the LHC.