In this paper, we present a new bit allocation procedure based on the approximation of the rate distortion (R-D) functions provided by our efficient lattice vector quantizer with pyramidal dead zone (DZLVQ). Here, we show that DZLVQ R-D functions can be efficiently fitted by an exponential model. This property leads to an analytical solution to the bit allocation problem which reduces significantly the complexity of our compression scheme. Furthermore, our method is highly parallelizable. Finally we show that it keeps the very good results in terms of visual quality of DZLQV, as it better preserves fine structures with respect to SPIHT and JPEG2000 at low rates.