1. A method of operating processing hardware, the method comprising: (a) accepting image data represented by an ordered series of digital signals representing a block of quantized coefficients of a transformed block of image data, the quantized transform coefficients each having a respective value, including a respective amplitude from a finite set of amplitudes consisting of the most likely-to-occur amplitude and at least one other amplitude, the at least one other amplitude including the second-most likely-to-occur amplitude; (b) using a position event identifying method executing on the processing hardware to identify position events that each include a cluster of at least one consecutive signal having any amplitude other than the most likely-to-occur amplitude, such that the position events define the relative positions and runlengths of the clusters and of any intervening runs of consecutive coefficients having the most likely-to-occur amplitude; (c) using an amplitude event identifying method executing on the processing hardware to identify the amplitudes of the signals having amplitudes other than the most likely-to-occur amplitude; and (d) encoding the identified position events and encoding the identified amplitude events by respective codewords, and encoding the signs of the amplitudes other than the most likely-to-occur amplitude in the identified amplitude events, such that for at least some of the identified position events and identified amplitude events, events containing a cluster of signals having more likely-to-occur signal amplitudes other than the most likely-to-occur amplitude are encoded by shorter codeword(s) than are events containing a cluster of signals having less likely-to-occur signal amplitudes other than the most likely-to-occur amplitude; and (e) outputting the codewords formed by the encoding, wherein the position event identifying method uses Cluster Runlength Identifying and the amplitude event identifying method uses Multi-Table Amplitude Event Identifying, Cluster Runlength Identifying including identifying events of a first kind, each event of the first run including a run of consecutive signals having the second-most-likely-to-occur amplitude, and identifying events of a second kind, each event of the second kind being a run of consecutive signals having the most likely-to-occur value, Multi-Table Amplitude Event Identifying including in each run of consecutive signals of value or values having other than the most-likely-to-occur amplitude, identifying amplitude events of at least one consecutive signal, an identified amplitude event including a sequence of at least one consecutive signal having the next most likely-to-occur amplitude that ends in a signal having other than the second-most likely-to-occur amplitude, or ascertaining that the amplitude event has only a signal having other than the second-most likely-to-occur amplitude, or ascertaining that the amplitude event has only a sequence of consecutive signals having the second-most likely-to-occur amplitude, each identified amplitude event defined by the length of the run of consecutive signals of amplitude value or values other than the most-likely-to-occur amplitude, the length of the sequence of at least one consecutive signal having the second-most likely-to-occur amplitude, and by the amplitude of the last signal in the run, the third amplitude event identifying method including, in each run of consecutive signals of value or values having other than the most-likely-to-occur amplitude, identifying amplitude events of a single signal having other than the most-likely-to-occur amplitude, or wherein the position event identifying method uses 2-D Cluster Length and Position Identifying, 2-D Cluster Length and Position Identifying including identifying position events that each includes a run of one or more consecutive signals having other than the most-likely-to-occur amplitude preceded by either no signals having the most-likely-to-occur amplitude, or a run of one or more consecutive zero-valued signals having the most-likely-to-occur amplitude, each position event identified by the runlengths of the preceding run of consecutive zero-valued signals having the most-likely-to-occur amplitude, including a runlength of 0, and the runlength of the run of consecutive signals having other than the most-likely-to-occur amplitude.