A speech synthesizer was developed that operates by summing exponentially damped sinusoids at frequencies and amplitudes corresponding to peaks derived from the spectrum envelope of the speech signal. The spectrum analysis begins with the calculation of a smoothed Fourier spectrum. A masking threshold is then computed for each frame as the running average of spectral amplitudes over an 800-Hz window. In a rough simulation of lateral suppression, the running average is then subtracted from the smoothed spectrum (with negative spectral values set to zero), producing a masked spectrum. The signal is resynthesized by summing exponentially damped sinusoids at frequencies corresponding to peaks in the masked spectra. If a periodicity measure indicates that a given analysis frame is voiced, the damped sinusoids are pulsed at a rate corresponding to the measured fundamental period. For unvoiced speech, the damped sinusoids are pulsed on and off at random intervals. A perceptual evaluation of speech produced by the damped sinewave synthesizer showed excellent sentence intelligibility, excellent intelligibility for vowels in /hVd/ syllables, and fair intelligibility for consonants in CV nonsense syllables.