  The angular distribution of $B\to K\bar\ell\ell$ ($\ell = e,\,\mu,\,\tau$)
depends on two parameters, the lepton forward-backward asymmetry, $A_{\rm
FB}^\ell$, and the flat term, $F_H^\ell$. Both are strongly suppressed in the
standard model and constitute sensitive probes of tensor and scalar
contributions. We use the latest experimental results for $\ell = \mu$ in
combination with the branching ratio of $B_s\to \bar\mu\mu$ to derive the
strongest model-independent bounds on tensor and scalar effective couplings to
date. The measurement of $F_H^\mu$ provides a complementary constraint to that
of the branching ratio of $B_s\to \bar\mu\mu$ and allows us---for the first
time---to constrain all complex-valued (pseudo-)scalar couplings and their
chirality-flipped counterparts in one fit. Based on Bayesian fits of various
scenarios, we find that our bounds even become tighter when vector couplings
are allowed to deviate from the standard model and that specific combinations
of angular observables in $B \to K^*$ are still allowed to be up to two orders
of magnitude larger than in the standard model, which would place them in the
region of LHCb's sensitivity.
