follows (for r$_{3}$ = 3): We emphasize the following points: As mentioned in Section II, for large tan β and low M$_{A}$ 0 , the B$_{d,s}$ mixing amplitudes can be significantly enhanced. Indeed, comparing the constraints of Eq. (2.4) to Table V, we obtain for r$_{3}$ = 3 (and tan β = 30, M$_{A}$ 0 = 200 GeV): The r$_{3}$ dependence of upper bounds on the supersymmetric contributions to B$_{d}$ and B$_{s}$ mixings is shown in Fig. 1. We consider scenarios with anarchical A -terms at the messenger scale: so that We insert the anarchical structure (5.13) into the expressions of the δ q parameters in Eq. (3.3). We then compare these predictions to the bounds given in the Tables I and II. Note that these bounds are obtained for m$_{˜}$ q = 1 TeV. Recalling that parametrically m 2 ˜ q ∼ r$_{3}$ ˜ m $^{2}$, we use ˜ m ∼ 1 TeV / √ r$_{3}$ . 16 ( X$_{q}$$_{A}$ )$_{ij}$ = O (1) , ( Z$_{A}$$_{q}$ )$_{ij}$ = O (1) . (5.13) ( A $^{u,d}$)$_{ij}$ ( m$_{M}$ ) ∼ √$_{r}$ ˜ m, (5.12) B$_{d}$ : | M susy 12 /M exp 12 | ∼ < 0 . 36 , B$_{s}$ : | M susy 12 /M exp 12 | ∼ < 0 . 05 . (5.11) Note that these systems do not depend on ˆ r$_{i}$ , and so are independent of y$_{b}$ . B$_{d}$ : | M susy 12 /M exp 12 | ∼ < 0 . 007 , B$_{s}$ : | M susy 12 /M exp 12 | ∼ < 0 . 002 , (5.10) D : | M susy 12 /M exp 12 | ∼ < 0 . 6 . • The bound in the D system comes from 〈 δ u 12 〉 and is r$_{3}$ independent. • For r$_{3}$ = O (1 − 10), the bound in the B$_{s}$ system comes from 〈 δ d 23 〉 . For r$_{3}$ = O (1 − 7) it scales with 3 /r$_{3}$ ; for r$_{3}$ > 7 it does not scale with r$_{3}$ . • For r$_{3}$ = O (1 − 10), the bound in the B$_{d}$ system comes from 〈 δ d 13 〉 . For r$_{3}$ = O (1 − 1 . 5) it scales with 3 /r$_{3}$ ; for r$_{3}$ > 1 . 5 it does not scale with r$_{3}$ . B. Anarchical A -terms