  In the absence of the QCD penguin contributions a measurement of the
time-dependent asymmetry in the decay $B^0(t)\to \pi^+\pi^-$ gives directly the
weak angle $\alpha$. Several bounds have been proposed in the literature on the
magnitude of the penguin effects on this determination, the prototype of which
is the isospin bound of Grossman and Quinn. It is pointed out that large strong
final state interactions could cause these bounds to overestimate the real
penguin effect. A new flavor SU(3) bound is proposed, requiring only the
charge-averaged branching ratios for $B^0\to \pi^+\pi^-$ and $B_s\to K^+K^-$,
which exactly takes into account all relevant amplitudes and electroweak
penguin effects. This bound on the penguin-induced error on the determination
of the weak phase $\alpha$ holds even without a knowledge of the direct CP
asymmetry in the $\pi^+\pi^-$ channel.
