  The measurements carried out at LEP and SLC projected us into the precision
era of electroweak physics. This has also been relevant in the theoretical
interpretation of LHCb and Belle measurements of rare $B$ semileptonic decays,
paving the road for new physics with the inference of lepton universality
violation in $R_{K^{(*)}}$ ratios. The simplest explanation of these flavour
anomalies -- sizeable one-loop contributions respecting Minimal Flavour
Violation -- is currently disfavoured by electroweak precision data. In this
work, we discuss how to completely relieve the present tension between
electroweak constraints and one-loop minimal flavour violating solutions to
$R_{K^{(*)}}$. We determine the correlations in the Standard Model Effective
Field Theory that highlight the existence of such a possibility. Then, we
consider minimal extensions of the Standard Model where our
effective-field-theory picture can be realized. We discuss how these solutions
to $b \to s \ell \ell$ anomalies, respecting electroweak precision and without
any new source of flavour violation, may point to the existence of a
$Z^{\prime}$ boson at around the TeV scale, within the discovery potential of
LHC, or to leptoquark scenarios.
