When designing narrow band resonant SPUDT devices, the excitation of undesired transverse modes may result both in extra ripple in the passband and in spurious response in the stop band. To avoid these issues, it was proposed to use an approach similar to the one used for bulk-acoustic-wave devices. The principle is to add a low-velocity region at the edge of the transducer. If this edge region is properly designed, the transducer supports a so-called piston mode, i.e., a mode having a flat transverse amplitude profile across the aperture. A P-matrix model is extended to account for transverse modes in SPUDTs. The model is used to analyze both regular and piston-mode devices. Different physical possibilities to implement the low-velocity region are investigated and compared. In particular, it was found important to design the transducer so that the acoustical sources and reflectors extend into the edge region to minimize the coupling to higher order modes. From these considerations, a new implementation for piston-mode devices is proposed and demonstrated on a GSM base station 199-MHz filter. Electrical measurements as well as acoustical wave fields measured with an optical interferometer are analyzed and compared with simulations.