  We classify LambdaQCD/mb power corrections to nonleptonic B-> M1 M2 decays,
where M1 and M2 are charmless non-isosinglet mesons. Using recent developments
in soft-collinear effective theory, we prove that the leading contributions to
annihilation amplitudes of O[alphas(mb) LambdaQCD/mb] are real. The leading
annihilation amplitudes depend on twist-2 and twist-3 three parton
distributions. A complex nonperturbative parameter from annihilation first
appears at O[alphas^2(sqrt{Lambda mb}) LambdaQCD/mb]. ``Chirally enhanced''
contributions are also factorizable and real at lowest order. Thus,
incalculable strong phases are suppressed in annihilation amplitudes, unless
the alphas(sqrt{Lambda mb}) expansion breaks down. Modeling the distribution
functions, we find that (11 +- 9)% and (15 +- 11)% of the absolute value of the
measured B-> K- pi+ and B-> K- K0 penguin amplitudes come from annihilation.
This is consistent with the expected size of power corrections.
