In some applications of Josephson junctions it is necessary to suppress the critical current and Fiske resonances with a relatively small magnetic field. The sidelobes of the Fraunhofer pattern can be suppressed by taking an appropriate shape for the junction. A suppression of the first sidelobe below 1% of the zero-field critical current is possible as was shown experimentally. However, Fiske resonances are still present. We investigated how an adaptation of the junction shape may suppress these resonances, still maintaining the suppression of the sidelobes of the Fraunhofer pattern. Measurements of the critical current and Fiske resonance heights as a function of the magnetic field for a junction with a special shape and an adapted specially shaped junction were performed. For both types of junctions, the sidelobes of the Ic(B) patterns are suppressed. No extra suppression of the IF(B) patterns due to the adaptation of the shape is observed.