  We revisit the azimuthal decorrelation $\delta\phi$ between a jet and a $Z$
boson produced at hadron colliders. Employing different recombination schemes
for the jets leads to significantly different NLL-resummed predictions for the
distribution of this quantity. Specifically when the jets are reconstructed
with the $E$-scheme (i.e., four-momentum addition) in the $k_t$ or anti-$k_t$
clustering algorithms, then the resummation becomes highly non-trivial due to
the presence of non-global and/or clustering logarithms. We evaluate these
logarithms analytically at two loops and numerically to all orders in the
large-$\mathrm{N_c}$ limit, and present a full NLL resummation of $\delta
\phi$. We extend the accuracy of the perturbative expansion of the resummed
distribution at fixed order to NNLL accuracy by including
$\mathcal{O}(\alpha_s)$ NLO corrections obtained with MadGraph5_aMC@NLO. We
compare our findings with results of various Monte Carlo event generators and
with experimental data from the CMS collaboration.
