  Theoretical errors in the extraction of alpha from B -> pi^+ pi^-, rho^+
rho^-, rho pi decays are usually given in terms of upper bounds on
alpha_eff-alpha obtained from isospin or from SU(3) relations, where alpha_eff
is measured through CP asymmetries. We show that mild assumptions about
magnitudes and strong phases of penguin and tree amplitudes (|P/T| < 1 and
|delta| < pi/2) in B -> pi pi and B -> rho rho, imply alpha_eff > alpha, thus
reducing by a factor two the error in alpha. Similarly, the assumptions
|p_+-/t_+-| < 1, |\delta_-| < pi/2 <|\delta_+| in B -> rho pi lead to a
cancellation between two terms in alpha_eff-alpha. Current data support these
conditions.
