We point out that in the minimal supersymmetric standard model terms from the mixing of Higgs and Goldstone bosons which are connected to the renormalization of tan β via Slavnov-Taylor identities give rise to corrections that do not vanish in the limit where the supersymmetric particles are much heavier than the Higgs bosons. These additional contributions have important phenomenological implications as they can lead to potentially large supersymmetric effects in ∆M d and to a significant increase of ∆Ms relative to the standard model prediction for a light pseudoscalar Higgs A 0 . We calculate all the missing one-loop pieces and combine them with the known effective nonholomorphic terms to obtain improved predictions for the B d,s -B d,s mass differences ∆M d,s and the branching ratios of B d,s → µ + µ − in the large tan β regime of the minimal supersymmetric standard model with minimal-flavor-violation.