Several speech processing applications such as digital hearing aids and personal communications devices are characterized by very tight requirements in power consumption, size, and voltage supply. These requirements are difficult to fulfill, given the complexity and number of functions to be implemented, together with the real time requirement and large dynamic range of the input signals. To meet these constraints, careful optimization should be done at all levels, ranging from algorithmic level, through system and circuit architecture, to layout and design of the cell library. The key points of this optimization are among others, the choice of the algorithms, the modification of the algorithms to reduce computational complexity, the choice of a fixed-point arithmetic unit, the minimization of the number of bits required at every node of the algorithm, and a careful match between algorithms and architecture. The optimization method is explained and then applied to two typical speech processing applications: noise reduction/speech enhancement for digital hearing aids and spectral analysis and quantization in the CELP FS1016 speech coder.