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This letter presents a method for estimating the quantization noise introduced by a nonuniform quantizer, like those used in the family of MPEG-2/4 AAC audio coders. The method is generalized for the case of estimating the mean squared or the maximum value of the quantization noise. Its use will allow the bit-allocation algorithm to be adapted to different coding scenarios, depending on the available number of bits. Using the proposed method, it is possible to implement a loopless bit-allocation algorithm, without the need for using any kind of iteration loops. This helps to dramatically reduce the computational complexity of the bit-allocation algorithm, making it easier to implement in real-time applications where computational power is limited.