  CP-violating asymmetries in the decay $B^0(t)\to \pi^+ \pi^-$ are a
potentially rich source of information about both strong and weak phases. In a
previous treatment by the present authors use was made of an assumption about
the relative magnitude of tree and penguin amplitudes contributing to this
process. This assumption involved an ambiguity in relating the tree amplitude
to the amplitude for $B \to \pi \ell \nu$. It is shown here that one can avoid
this assumption, which adopted a particular convention for tree and penguin
amplitudes, and that the results are convention-independent.
