We update the constraints on new-physics contributions to Delta F = 2 processes from the generalized unitarity triangle analysis, including the most recent experimental developments. Based on these constraints, we derive upper bounds on the coefficients of the most general Delta F = 2 effective Hamiltonian. These upper bounds can be translated into lower bounds on the scale of new physics that contributes to these low-energy effective interactions. We point out that, due to the enhancement in the renormalization group evolution and in the matrix elements, the coefficients of non-standard operators are much more constrained than the coefficient of the operator present in the Standard Model. Therefore, the scale of new physics in models that generate new Delta F = 2 operators, such as next-to-minimal flavour violation, has to be much higher than the scale of minimal flavour violation, and it most probably lies beyond the reach of direct searches at the LHC.