For more than a decade it has been known, in a qualitative way, that the long‐time average power of a speech signal in an amplitude‐limited communications system can be increased materially by clipping the peaks of the speech wave and amplifying the remainder until the new peaks have the maximum allowable amplitude. This power increase can be computed from the statistical distribution for the instantaneous amplitudes of speech. Some of the available distributions have been collected and compared, and, upon their showing good agreement, one of them has been used for the computation. Simple formulas show that the power increase can be neither greater than the amount of clipping nor greater than the peak factor of speech. For 24 db of peak clipping, the power gain is about 12 db. The exact value depends upon the choice of peak factor for unclipped speech. In practice, the actual gain in signal‐to‐noise ratio on peak‐limited communications systems (e.g., AM and DSB radio) will be less than that computed here.