Bs-B̄s mixing has been measured recently by D0 and CDF. The range predicted in the standard model is consistent with data. However, the standard model central values for ΔMBs and also ΔMBd are away from the data which may be indications of new physics. Using the observed values of ΔMBs and ΔMBd we study general constraints on flavor changing Z′ interactions. In models with nonuniversal Z′ couplings we find that significant enhancements over the standard model are still possible in the rare decay modes B→Xsτ+τ-, B→Xsνν̄ and Bs→τ+τ-. Tree-level Z′ contributions to K→πνν ̄ are now constrained to be very small, but one-loop effects can still enhance the standard model rate by a factor of 2.