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This paper discusses a variable bit rate speech coding system based on explicit coding of the reconstruction noise in ADPCM (differential pulse code modulation with adaptive quantization). If the ADPCM bit rate is R bits/sample, PCM coding of its noise using an average bit rate of Rn bits/sample provides the receiver with the possibility of operating at any bit rate in the range R to R + max {Rn}. Using R values in the range 2 to 5, and Rn values in the range 0 to 3, we compare the performance of the (R + Rn)‐bit system with that of conventional (R + Rn)‐bit ADPCM. If noise coding is based on instantaneous Rn‐bit quantization of its samples with an optimized step size, the signal‐to‐noise ratio performance is comparable to that of conventional ADPCM for Rn = 1, but it deteriorates significantly for Rn > 1. With non‐instantaneous noise coding, the performance can exceed that of conventional ADPCM for any Rn > 1, if R > 2. This is due to a variable bit allocation algorithm that quantizes noise samples with differing resolutions, while maintaining a constant total bit rate in every block of 4 ms. The algorithm does not require the transmission of any extra side information. It can also be regarded as a way of improving the performance of ADPCM coding at a single bit rate of R + Rn bits/sample.