In this chapter we introduce a class of fractal image coders which have the remarkable property of giving exact decoder convergence in the lowest possible number of iterations (which is image independent). The class is related to that introduced by Jacquin [45,46,47,48], employing simple affine mappings working in a blockwise manner. The resulting decoder can be implemented in a pyramid-based fashion, yielding a computationally very efficient structure. Also, a coder offering non-iterative decoding and direct attractor optimization in the encoder is included as a special case. Other benefits of the proposed coder class include more optimal quantization and an improved Collage Theorem.