Naturally Small $x_s$?

Within the Standard Model, $x_s$ (the mixing parameter in the $B_s-\bar B_s$ system) is constrained to the range $7 \leq x_s\leq 40$. We point out that if New Physics contributes significantly to $x_d$ (the mixing parameter in the $B_d-\bar B_d$ system), then $2 \leq x_s\leq 7$ is possible without any fine-tuned cancellations between the Standard Model and the New Physics contributions.