1. A method of operating processing hardware for processing an ordered series of digital signals that each have 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 a next most likely-to-occur amplitude to the most likely-to-occur amplitude, the method comprising: (a) accepting the ordered series of digital signals representing a block of quantized coefficient of a transformed block of image data; (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 included in the identified position events 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 respective amplitudes other than the most likely-to-occur amplitude; (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-Dimensional Amplitude Event Identifying, wherein Cluster Runlength Identifying includes identifying events of a first kind, each event of the first kind including a run of consecutive signals having the next-to-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, and wherein Multi-Dimensional Amplitude Event Identifying includes identifying events that each include a run of one or more consecutive signals having other than the most likely-to-occur amplitude, such that encoding an identified amplitude event includes jointly encoding a plurality of consecutive signals having amplitude other than the most likely-to-occur amplitude that is included in the identified amplitude event.