ITU-T G.726 ADPCM has traditionally been considered a toll-quality coder and has been deployed ubiquitously in the public switched telephony network (PSTN). Currently, it is also being considered as the baseline means for carrying voice over connection-oriented packet networks, such as ATM and frame relay. At a high coding rate of 32 kbit/s, however, ITU-T G.726 ADPCM may still produce coded signals with annoying quantization noises. This paper proposes using two perceptually motivated approaches to enhance the performance of ITU-T G.726 ADPCM: (1)noise spectral shaping at the encoder; and (2)adaptive postfiltering at the decoder output. Based on listening experiments, we found that the combined system at various bit rates (16, 24, 32 kbit/s) consistently outperform G.726 ADPCM of the same bit rate. In particular, the combined system operating at 32 kbit/s consistently outperforms ITU-T 16 kbit/s G.728 LD-CELP. At 24 kbit/s, the performance is very close to G.728 LD-CELP and/or G.726 ADPCM at 32 kbit/s.