  We study the effects of new-physics contributions to B --> pi pi decays,
which can be parametrized as four new complex quantities. A simple analysis is
provided by utilizing the reparametrization invariance of the decay amplitudes.
We find that six quantities can be reabsorbed into the definitions of Standard
Model-like parameters. As a result, the usual isospin analysis provides only
two constraints on new physics which are independent of estimates for the
Standard Model contributions. In particular, we show that one is not sensitive
to new physics affecting the I=0 amplitudes. On the other hand, I=2 new physics
can be detected, and its parameters can be measured by using independent
determinations of the weak phases. We obtain constraints on these new-physics
parameters through a fit to the current experimental data.
