  We discuss a method for extracting CP phases from pairs of B decays which are
related by flavor SU(3). One decay (B0 -> M1 M2) receives a significant bbar ->
dbar penguin contribution. The second (B' -> M1' M2') has a significant bbar ->
sbar penguin contribution, but is dominated by a single amplitude. CP phase
information is obtained using the fact that the B' -> M1' M2' amplitude is
related by SU(3) to a piece of the B0 -> M1 M2 amplitude. The leading-order
SU(3)-breaking effect (~25%) responsible for the main theoretical error can be
removed. For some decay pairs, it can be written in terms of known decay
constants. In other cases, it involves a ratio of form factors. However, this
form-factor ratio can either be measured experimentally, or eliminated by
considering a double ratio of amplitudes. In all cases, one is left only with a
second-order effect, ~5%. We find twelve pairs of B decays to which this method
can be applied. Depending on the decay pair, we estimate the total theoretical
error in relating the B' -> M1' M2' and B0 -> M1 M2 amplitudes to be between 5%
and 15%. The most promising decay pairs are Bd -> pi+ pi- and Bu+ -> K0 pi+,
and Bd -> D+ D- and Bd -> Ds+ D- or Bu+ -> Ds+ D0bar.
