The transmission of speech through difficult channels is more easily accomplished if the complicated speech waveform can be simplified. One method of simplification is to "infinitely clip" the speech to a rectangular signal which preserves only the original zero-crossings. Early research with clipped speech and clipped, differentiated speech is extended to clipped, twice differentiated speech and an "enriched" mixture of two clipped derivatives of different order. The two new systems produce a higher quality signal than the earlier methods, the "enriched" speech approaching typical communications quality. Data is presented comparing the intelligibility of these four systems. A scheme for preserving simultaneously the exact times of both zeros and extremals is discussed in detail and experimentally investigated. The intelligibility of time-quantized, second-order clipped. speech is studied, and certain statistical parameters of the clipped signals measured. These data indicate: that a three-to-one reduction in bit rate over telephonic PCM is possible while still preserving tolerable intelligibility. .