  Defining a most economical parametrization of time-dependent B-> rho^\pm
pi^\mp decays, including a measurable phase alpha_{eff} which equals the weak
phase alpha in the limit of vanishing penguin amplitudes, we propose two ways
for determining alpha in this processes. We explain the limitation of one
method, assuming only that two relevant tree amplitudes factorize and that
their relative strong phase, delta_t, is negligible. The other method, based on
broken flavor SU(3), permits a determination of alpha in B^0-> rho^\pm pi^\mp
in an overconstrained system using also rate measurements of B^{0,+}-> K^* pi
and B^{0,+}->rho K. Current data are shown to restrict two ratios of penguin
and tree amplitudes, r_\pm, to a narrow range around 0.2, and to imply an upper
bound |alpha_{eff} - alpha| < 15 degrees. Assuming that delta_t is much smaller
than 90 degrees, we find alpha =(93\pm 16) degrees and (102 \pm 20) degrees
using BABAR and BELLE results for B(t)-> rho^\pm pi^mp. Avoiding this
assumption for completeness, we demonstrate the reduction of discrete
ambiguities in alpha with increased statistics, and show that SU(3) breaking
effects are effectively second order in r_\pm.
