Previously reported experiments have indicated that computer enhancement of single channel speech in wideband noise generally does not result in increased intelligibility. Our research goal has been to investigate the effect of such enhancement on speech quality. Our experimental framework employed natural speech degraded by additive white, non‐white, and aircraft cockpit noise over a wide range of signal‐to‐noise ratios (− 15 to 20 dB). An iterative enhancement technique based on a method reported by Lim and Oppenheim, was generalized to allow nonwhite additive noise. Spectral estimates of the noise were made using maximum‐likelihood method, maximum‐entropy method, Burg's method, periodogram, Bartlett's method, and Pisarenko harmonic decomposition. Quality was estimated using a variety of objective measures which have been shown to correlate well with subjective quality scores resulting from the diagnostic acceptibility measure (DAM). Over a large number of noise conditions the best objective qualities resulted when Bartlett, Burg, and maximum‐entropy spectra were used. In general, significant improvements in terms of objective measures were observed when enhancement took place. [Work supported by Lockheed Georgia Company.]