  We consider hadronic transitions from the $h_b(2P)$ bottomonium resonance to
lower states of bottomonium with emission of either $\omega$ meson, or two
pions, or $\eta$ meson. For the former two transitions the branching ratios are
related to similar transitions from $\chi_{b1}(2P)$ and the recently measured
by Belle fractions of the radiative decays of $h_b(2P)$. We argue that the
fraction of the $h_b(2P)$ total decay rate remaining for the annihilation rate
is on the verge of contradiction with the `parton' picture of bottomonium
annihilation resulting in similarity between the decays of $h_b(1,2P)$ and
$\chi_{b1}(1,2P)$. The contradiction gets even stronger, if the transition
$h_b(2P) \to \Upsilon(1S) \, \eta$ has branching fraction of a few percent or
more. We argue that, although quite uncertain, the latter fraction may indeed
be that significant.
