We develop a new method for finding upper bounds for Bermudan swaptions in a swap-rate market model. By comparing with lower bounds found by exercise boundary parametrization, we find that the bounds are well within bid-offer spread. As an application, we study the dependence of Bermudan swaption prices on the number of instantaneous factors used in the model. We also establish an equivalence with LIBOR market models and show that virtually identical lower bounds for Bermudan swaptions are obtained.