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.
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