  The measurement of $B_s$-meson branching fractions is a fundamental tool to
probe physics beyond the Standard Model. Every measurement of untagged
time-integrated $B_s$-meson branching fractions is model-dependent due to the
time dependence of the experimental efficiency and the large lifetime
difference between the two $B_s$ mass eigenstates. In recent measurements, this
effect is bundled in the systematics. We reappraise the potential numerical
impact of this effect -- we find it to be close to 10% in real-life examples
where new physics is a correction to dominantly Standard-Model dynamics. We
therefore suggest that this model dependence be made explicit, i.e. that $B_s$
branching-fraction measurements be presented in a two-dimensional plane with
the parameter that encodes the model dependence. We show that ignoring this
effect can lead to over-constraining the couplings of new-physics models. In
particular, we note that the effect also applies when setting upper limits on
non-observed $B_s$ decay modes, such as those forbidden within the Standard
Model.
