  The extraction of the CKM angle $\alpha$ from the asymmetry in $B^0 \to
\pi^+\pi^-$ vs ${\bar B^0} \to \pi^+\pi^-$ suffers from a currently unknown
penguin contribution. Experimentally, one can determine the magnitude and phase
of the CP asymmetry from a time-dependent analysis of tagged events, and the
average rate for $B^0$ and $\bar{B}^0$ decays to $\pi^+\pi^-$ from untagged
events. These measurements, together with the magnitudes and relative phase of
the tree and penguin diagrams, can in principle completely determine $\alpha$,
free of discrete ambiguities. We perform an error analysis on $\alpha$ given
assumptions on the values and uncertainties of both the measurements and
theoretical inputs.
