A DWT unit applies wavelet transform to an input signal to output transform coefficients, and a quantization unit quantizes those transform coefficients with a quantization step size determined according to target image quality. Then, a rate control unit controls the rate of coded data according to information on the quantization step size. Also, an image-quality control unit controls the rate of only part of coded data which is determined from a priority table. This achieves a compression encoder which operates at high speed with minimal operations.