Most of compressible turbulence models developed so far were focused on the free shear layer predictions and, hence, were not suitable for wall-bounded compressible flows. To remedy this dilemma, we need a compressibility parameter that works well for both wall-bounded and free shear layers. Such a parameter was suggested by Yoshizawa et al. (AIAA J. 41 (6) (2003), pp. 1029-1036; Phys. Fluids 18 (2006), pp. 1-17) which was a combination of the turbulent Mach number and a non-equilibrium parameter. This paper presents a modified version of our previous model (J Turbul. 6 (2) (2005), pp. 1-25), which worked well for compressible mixing layer and successfully reproduced the anisotropy of the Reynolds stresses but was not suitable for wall boundary layer predictions as the model involves only the turbulent Mach number. In the new model we propose, we modify our earlier compressibility parameter by adopting the non-equilibrium parameter of Yoshizawa et al. (AIAA J. 41 (6) (2003), pp. 1029-1036; Phys. Fluids 18 (2006), pp. 1-17). The proposed model is found to predict adequately the Reynolds stress anisotropy and the growth rate of a mixing layer, and also to work properly for a supersonic boundary layer.