1. A method of operating an encoding apparatus, the method comprising: for an ordered sequence of quantized transform coefficients of a block of image data, the quantized transform coefficients having respective amplitudes including a most likely-to-occur amplitude and at least one other amplitude, and for a selected low-frequency variable length coding method that includes recognizing events that each includes a cluster of coefficients having respective amplitudes other than the most likely-to-occur amplitude, determining a set of candidate breakpoints, each candidate breakpoint being defined by an ending event location for position events recognized in using the selected low-frequency variable length coding method, any candidate breakpoints that defines a position after the start of the sequence being for a hybrid coding method that includes using the selected low-frequency coding method until the ending event, and using a selected high-frequency method to encode a part of the sequence starting from immediately after the ending event; for each candidate breakpoint, determining a weighted sum of the number of clusters of coefficients with other than the most likely-to-occur amplitude having each cluster length possible for the candidate breakpoint, the weighted sum using, for the number of clusters having a particular cluster length, a weighting that is an amount proportional the particular cluster length; selecting as the breakpoint to use a candidate breakpoint that maximizes the weighted sum of numbers of clusters of each cluster length; encoding the sequence including encoding a first portion of the sequence up to and including the final ending event defined by the selected breakpoint using the selected low-frequency variable length coding method and encoding a second portion of the sequence from the first coefficient after the final ending event to the end of the sequence using the selected high-frequency variable length coding method.