An image data compression technique is described which utilizes calculating means and a selected series of bit calculating stages having delays, to estimate one or more quantization parameters for such data. The estimation process preferably is iterated a number of times, with the values found through each estimation being used as the trial values for subsequent estimations. In addition, an initial trial value is selected by a data look ahead technique, which assures that its value is within range of the final quantization parameter used to quantize the data. The final quantization parameter insures that the compressed data fits within a predetermined number of encoded data bits to be transmitted or recorded, for example, in a recording medium.