  The 2.5 sigma discrepancy between theory and experiment observed in the
difference A_CP(B^- --> pi^0 K^-)-A_CP(Bbar^0 --> pi^+ K^-) can be explained by
a new electroweak penguin amplitude. Motivated by this result, we analyse the
purely isospin-violating decays B_s --> phi rho^0 and B_s --> phi pi^0, which
are dominated by electroweak penguins, and show that in presence of a new
electroweak penguin amplitude their branching ratio can be enhanced by up to an
order of magnitude, without violating any constraints from other hadronic B
decays. This makes them very interesting modes for LHCb and future B factories.
We perform both a model-independent analysis and a study within realistic New
Physics models such as a modified-Z^0-penguin scenario, a model with an
additional Z' boson and the MSSM. In the latter cases the new amplitude can be
correlated with other flavour phenomena, such as semileptonic B decays and
B_s-Bbar_s mixing, which impose stringent constraints on the enhancement of the
two B_s decays. In particular we find that, contrary to claims in the
literature, electroweak penguins in the MSSM can reduce the discrepancy in the
B --> pi K modes only marginally. As byproducts we update the SM predictions to
Br(Bbar_s --> phi pi^0)=1.6^{+1.1}_{-0.3}*10^{-7} and Br(Bbar_s --> phi
rho^0)=4.4^{+2.7}_{-0.7}*10^{-7} and perform a state-of-the-art analysis of B
--> pi K amplitudes in QCD factorisation.
