Progress is reported in the development of a nonlinear Reynolds-stress-transport model for compressible, turbulent flow. The focus is on a variation of a particular cublc model that does not require the usual topography-related parameters, such as normal-to-wall vectors. However, certain wall-proximity corrections that have been used in the model to replace conventional wall-reflection terms display the wrong response to shocks, which are falsoly interpreted as localized regions of strong inhomogeneity. A modified cubic variant is proposed that allows integration across the semiviscous sublayer and incorporates additional constraints to guard against unphysical response of the pressure-strain model in the vicinity of shock waves. The modified model is applied to both two- and three-dimensional compressible flows, involving shock-wave/boundary-layer interaction, and is shown to yield generally favorable results