1. In a digital compression encoder responsive to an array of a relatively large number of multibit coefficients defining image data at a relatively high resolution that has been hierarchical subband decomposed by a wavelet transform at a given plurality of lower resolutions, whereby the lowest low (LL) subband comprises an array having the smallest number of multibit coefficients of all the wavelet-transform subband arrays, each LL subband multibit coefficient comprises an ancestor of all multibit coefficients of all higher subbands descended from that LL subband multibit coefficient, and each of said multibit coefficients of said LL subband and said multibit coefficients of said descendents thereof includes a most significant bit; wherein said encoder includes coding means for deriving a data-compressed code comprising (a) a ZEROTREE symbol at first given coordinates of of said LL subband or at coordinates of descendents of said first given coordinates of said LL subband which are occupied by coefficients that are zerotree roots, (b) an ISOLATED ZERO symbol at second given coordinates of of said LL subband or at coordinates of descendents of said second given coordinates of said LL subband which are occupied by isolated-zero coefficients, and (c) at least one type of non-zero symbol at third given coordinates of said LL subband or at coordinates of descendents of said third given coordinates of said LL subband which are occupied by non-zero coefficients; the improvement for efficiently deriving said data-compressed code wherein said encoder comprises: means responsive to each multibit coefficient of said LL subband and said multibit coefficients of all of its descendents of said wavelet transform for deriving a zerotree map, wherein said zerotree map includes a zerotree-map multibit coefficient corresponding to each coefficient of said LL subband array, and each zerotree-map coefficient has a binary "1" value in a bit position thereof only if either its corresponding LL-subband-array coefficient or any of the descendents of its corresponding LL-subband-array coefficient has its most significant bit in that bit position; and said coding means includes means that starts with a list of coordinates of said relatively small number of coefficients of said LL subband of said array and a relatively high initial threshold value for dynamically deriving in sequence said data-compressed code from the multibit coefficients of the wavelet-transform subband and the multibit coefficients of the zerotree map first at said relatively high initial threshold value and then at one or more successively lower threshold values by ignoring from consideration in said sequential dynamic derivation all coordinates of coefficients which are descendents of coordinates which have already been found in said sequential dynamic derivation to be occupied by coefficients that are zerotree roots.