  In current searches for D0 anti-D0 mixing, the time evolution of
``wrong-sign'' decays is used to distinguish between a potential mixing signal
and the dominant background from doubly-Cabibbo-suppressed decays. A term
proportional to $\Delta Mt$ in the expression for the time evolution is often
neglected in theoretical discussions and experimental analyses of these
processes. We emphasize that, in general, this term does not vanish even in the
case of CP invariance. Furthermore, CP invariance is likely to be violated if
the rate of D0 anti-D0 mixing is close to the experimental bound. The
consequence of either of these two facts is that the strongest existing
measured bound is not applicable for constraining New Physics.
