  A width difference of the order of 20\% has previously been predicted for the
two mass eigenstates of the $B_s$ meson. The dominant contributor to the width
difference is the $b\rightarrow c\bar c s$ transition, with final states common
to both $B_s$ and $\overline{B}_s$. All current experimental analyses fit the
time-dependences of flavor-specific $B_s$-modes to a single exponential, which
essentially determines the average $B_s$ lifetime. We stress that the same data
sample allows even the measurement of the width difference. To see that, this
note reviews the time-dependent formulae for tagged $B_s$ decays, which involve
rapid oscillatory terms depending on $\Delta mt$. In untagged data samples the
rapid oscillatory terms cancel. Their time-evolutions depend only on the much
more slowly varying exponential falloffs. We discuss in detail the extraction
of the two widths, and identify the large (small) CP-even (-odd) rate with that
of the light (heavy) $B_s$ mass eigenstate. It is demonstrated that decay
length distributions of some \underline{untagged} $B_s$ modes, such as $\rho^0
K_S, \; D_s^{(*)\pm}K^{(*)\mp}$, can be used to extract the notoriously
difficult CKM unitarity triangle angle $\gamma$. Sizable CP violating effects
may be seen with such untagged $B_s$ data samples. Listing $\Delta\Gamma$ as an
observable allows for additional important standard model constraints. Within
the CKM model, the ratio $\Delta\Gamma/ \Delta m$ involves no CKM parameters,
only a QCD uncertainty. Thus a measurement of $\Delta\Gamma \;(\Delta m)$ would
predict $\Delta m \;(\Delta\Gamma )$, up to the QCD uncertainty. A large width
difference would automatically solve the puzzle of the number of charmed
hadrons per $B$ decay in favor of theory. We also derive an upper limit of $(|
\Delta\Gamma | / \Gamma)_{B_s} <~ 0.3$. Further, we must abandon the notion of
branching fractions of $B_s\rightarrow f$, and instead consider $
B(B^0_{L(H)}\rightarrow f)$, in analogy to the neutral kaons.
