Techniques for estimating distortion due to quantization of data are described. A histogram with multiple bins may be obtained for a set of coefficients to be quantized. Distortion due to quantization of the set of coefficients may be estimated based on the histogram and average distortions for the histogram bins. The number of coefficients in each bin may be multiplied with an average distortion for the bin to obtain a per-bin distortion. The per-bin distortions for all of the bins may be accumulated and scaled with a correction factor to obtain the estimated distortion. The techniques may be used to estimate distortions for a set of coding elements. Distortion and rate may be estimated for each coding element for each of multiple quantization steps. A set of quantization steps may be selected for the set of coding elements based on the estimated distortions and the estimated rates for the set of coding elements for different quantization steps.