Abstract: Improved methods and apparatus for implementing JPEG 2000 MQ encoding operations are described. The following features of the invention may be used alone or in combination to implement JPEG 2000's coefficient bit modeling 1) Lists of coefficients to be processed in one or more subsequent coding passes are generated as coefficients are processed. The list is allows processing in the subsequent coding pass to be limited to coefficients on the list; and 2) Generation, updating and use of a neighborhood descriptor value table that stores a neighborhood descriptor value for each coefficient of a block being processed. The neighborhood descriptor values provide information about the state of the coefficient and its adjacent neighbors. Neighborhood descriptor values are used to access a lookup table that provides one or more context values and/or sign value to be used in MQ encoding.