1. A method of operating processing hardware, the method comprising: (A) recognizing in a bitstream of codewords one or more codewords for a particular ordered series of quantized transform coefficients of a particular block of image data, the bitstream representing a plurality of ordered series of quantized transform coefficients of blocks of image data, each ordered series corresponding to one block of the image data, each quantized transform coefficient having a respective amplitude from a finite set of amplitudes consisting of a most likely-to-occur amplitude and at least one other amplitude, the at least one other amplitude including a second-most likely-to-occur amplitude, the one or more codewords identifying the position in the particular ordered series of any cluster of at least one quantized coefficient having other than the most likely-to-occur amplitude, the one or more codewords further defining the amplitudes of the quantized coefficients having amplitudes other than the most likely-to-occur amplitude, wherein the codewords for the particular ordered series are determined from the particular ordered series of quantized transform coefficients by a position event identifying method to identify for each series representing a block of image data, one or more position events that each includes a cluster of one or more consecutive quantized coefficients having other than the most likely-to-occur amplitude preceded by either no quantized coefficients having the most likely-to-occur amplitude, or a run of one or more consecutive quantized coefficients having the most likely-to-occur amplitude, each position event identified by the runlengths of the preceding run of consecutive quantized coefficients having the most likely-to-occur amplitude, including a runlength of 0, and the runlength of the cluster of consecutive quantized coefficients having other than the most likely-to-occur amplitude, and an amplitude-event-identifying method to identify amplitude events defining for each series representing a block of image data the amplitudes of the quantized coefficients having amplitudes other than the most likely-to-occur amplitude, and a coding method that forms codewords for the position events and amplitude events; wherein the coding of the coding method is characterized in that for at least some identified position and amplitude events, the more likely to occur the position and amplitude events, the shorter the codewords that encode the position and amplitude events; and (B) determining from the recognized codewords the position in the particular ordered series of any cluster of quantized coefficients having other than the most likely-to-occur amplitude and the amplitude of each quantized coefficients in the particular series.