It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.