  We calculate CP-violating rates and asymmetry parameters in charged and
neutral $B\to \pi\pi, \pi K$ and $\bar K K$ decays arising from the
interference of tree and penguin (strong and electroweak) amplitudes with
different strong and CKM phases. The perturbative strong (electroweak) phases
develop at order $\alpha_s$ ($\alpha_{em}$) from absorptive parts of one-loop
matrix elements of the next-to-leading (leading) logarithm corrected effective
Hamiltonian. The BSW model is used to estimate the hadronic matrix elements.
Based on this model, we find that the effect of strong phases and penguins is
substantial in most channels, drastic in many. However, a measurement of the
time dependence parameter $a_{\epsilon+\epsilon'}$ in the $\pi^+\pi^-$ channel
is only influenced at the 20\% level by the complication of the penguins.
Recent flavor sum rules developed for $B^{0,\pm} \rightarrow \pi\pi, \pi K, K
\bar K$ amplitudes are tested in this model. Some are well satisfied, others
badly violated, when electroweak penguins are included.
