  We propose a model for diffusion-limited annihilation of two species, $A+B\to
A$ or $B$, where the motion of the particles is subject to a drift. For equal
initial concentrations of the two species, the density follows a power-law
decay for large times. However, the decay exponent varies continuously as a
function of the probability of which particle, the hopping one or the target,
survives in the reaction. These results suggest that diffusion-limited
reactions subject to drift do not fall into a limited number of universality
classes.
