A closure for the compressible portion of the pressure strain covariance is developed. It is shown that, within the context of a pressure strain closure assumption linear in the Reynolds stresses, an expression for the pressure dilatation can be used to construct a representation for the pressure strain. Additional closures for the unclosed terms in the Favre Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections are consistent with current DNS results. Using the compressible pressure strain and mean acceleration closures in the Favre Reynolds stress equations an algebraic closure for the Favre Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Favre Reynolds stress closure and two equation algebraic models are compared to laboratory data. The mixing layer configuration computations are compared to laboratory data; since the laboratory data for the turbulence stresses is inconsistent, this comparison is inconclusive. Comparisons for the spread rate reduction indicate a sizable decrease in the mixing layer growth rate.