  Recent improvements to the limit of Delta M_{B_s} imply that pure superweak
theories, while not excluded, no longer provide a good fit to the data. A class
of general superweak theories is introduced in which all flavor changing
interactions are governed by an approximate flavor symmetry which gives a ``3
mechanism''. These theories are in good agreement with data, and predict low
values for |V_{td}|, |V_{ub}/V_{cb}|, B(K^+ to pi^+ nu nubar), epsilon'/epsilon
and CP asymmetries in B decays, and high values for Delta M_{B_s} and f_B
sqrt{B_B}. An important example of such a theory is provided by weak scale
supersymmetric theories with soft CP violation. The CP violation originates in
the squark mass matrix, and, with phases of order unity, flavor symmetries can
yield a correct prediction for the order of magnitude of epsilon_K.
