Optimum nonnegative integer bit allocation (ONIBA) is a conspicuous technique, which usually provides the solution of optimal quantization issues for the transform coders (TCs). In order to obtain the optimum bits for a specific quantizer, all the existing ONIBA algorithms strongly rely on the variance characteristics of transform coefficients. Typically, in the wavelet-based TCs, the sub-band variances are directly estimated in the wavelet domain. This direct variance estimation is not supposed to be the best way to obtain the exact variance information, because the practical values of the wavelet coefficients may not be precise and therefore constitute an uncertain environment for the accurate variance estimation. Consequently, all the existing ONIBA algorithms often exhibit poor quantization performance in the presence of entropy coder. Hence, this paper presents a new fuzzy domain variance estimation and refinement (FDVER)-based ONIBA algorithm to attain the real optimum quantization of the wavelet coefficients in the presence of entropy coder. The outcome shows that the proposed FDVER-ONIBA algorithm outperforms and provides high-quality image compression along with the significant bitrate savings by the efficient quantization of the wavelet coefficients as compared to the existing common sub-band coding technique and the recent ONIBA algorithms.