  The CLEO collaboration has recently reported a (first) measurement of $BR (B
\to \pi^+ \pi^-) = (4.7^{+1.8}_{-1.5} \pm 0.6) \times 10^{-6}$. We study, using
recent results on QCD improved factorization, the implications of this
measurement for the determination of the CKM phase $\alpha$ and also for the
rate for $B \to \pi^0 \pi^0$. If the $B \to \pi^-$ form factor is large
$(\stackrel{>}{\sim} 0.3)$, then we find that the CLEO measurement favors small
$|V_{ub}/V_{cb}|$ so that the expected error (due to neglecting the QCD penguin
amplitude) in the measurement of $\alpha$ using {\em only} the time-dependent
analysis of the decay $B \to \pi^+ \pi^-$ is large $\sim 15^{\circ}$. However,
if $|V_{ub}/V_{cb}|$ is known, then it is possible to determine the correct
value of $\sin 2 \alpha$.
