We present a model for compressible sub-Alfvenic isothermal magnetohydrodynamic ( MHD) turbulence in low-beta plasmas and numerically test it. We separate MHD fluctuations into three distinct families: Alfven, slow, and fast modes. We find that production of slow and fast modes by Alfvenic turbulence is suppressed. As a result, Alfven modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfven modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.