  We scrutinize the recently further strengthened hints for new physics in
semileptonic $B$-meson decays, focusing on the 'clean' ratios of branching
fractions $R_K$ and $R_{K^\ast}$ and examining to which pattern of new effects
they point to. We explore in particular the hardly considered, yet fully
viable, option of new physics in the right-handed electron sector and
demonstrate how a recently proposed framework of leptons in composite Higgs
setups naturally solves both the $R_K$ and $R_{K^\ast}$ anomalies via a
peculiar structure of new physics effects, predicted by minimality of the model
and the scale of neutrino masses. Finally, we also take into account further
observables, such as ${\cal B}(B_s \to \mu^+\mu^-)$, $\Delta M_{B_s}$, and
angular observables in $B \to K^{\ast} \mu^+ \mu^-$ decays, to arrive at a
comprehensive picture of the model concerning (semileptonic) $B$ decays. We
conclude that -- since it is in good agreement with the experimental situation
in flavor physics and also allows to avoid ultra-light top partners -- the
model furnishes a very promising scenarios of Higgs compositeness in the light
of LHC data.
