  The parameter $y_{CP}$ is used to characterize mixing in the
$D^0$-$\bar{D}{}^0$ meson system. To determine $y_{CP}$, one measures the
effective decay width of a $D^0$ or $\bar{D}{}^0$ decaying to a $CP$
eigenstate, relative to the effective width for a decay to a Cabibbo-favored,
flavor-specific final state. When using $y_{CP}$ to extract information about
$D^0$-$\bar{D}{}^0$ mixing and $CP$ violation, the decay width of the
Cabibbo-favored decay is usually assumed to equal $1/\tau$, the reciprocal of
the $D^0$ lifetime. However, there is a small correction to this that should be
taken into account when $y_{CP}$ is measured with sufficiently high precision.
We calculate this correction in terms of charm mixing and $CP$ violation
parameters $x$, $y$, $|q/p|$, and $\phi$.
