In an integrated radar and communication system, the filter output of each pulse of the integrated radar and communication waveform usually has high sidelobe level (SLL) and signal-to-noise ratio (SNR) loss as well as serious range sidelobe modulation (RSM). To solve these problems, a joint weighted optimization (JWO) method is proposed to design the filters. In this method, the filters for different integrated radar and communication waveforms are designed by jointly minimizing the RSM, SNR loss, and SLL according to different practical demands. In terms of the RSM, SNR loss, and SLL, the performance of the designed filters is tunable by reasonably changing the weight factors. Finally, several numerical results are presented to verify the effectiveness of the proposed method.