A new wavelet-based L-infinite-constrained fixed and embedded coding technique is proposed in this paper. For any desired distortion bound, the embedded bit stream can be truncated at a corresponding bit-rate, for which the required upper bound on the individual elements of the reconstruction error signal is guaranteed. The original signal can also be coded up to a fixed a priori user-defined distortion bound, ranging up to lossless coding. The proposed coding technique supports both 2D (images) and 3D (volumetric) input data.