In a randomly packed unconsolidated granular medium, there is a random asymmetry in mechanical coupling between grains that has been shown to cause an increase in the effective inertia, hence a reduction in sound and shear wave speeds [N. P. Chotiros and M. J. Isakson, J. Acoust. Soc. Am., 121, EL70–EL76 (2007)]. The increase in inertia for shear waves is revisited because, in addition to the incoherent motion due to the random asymmetry, there is an additional component due to coherent grain rotation. Shear wave speed is predicted to be dependent on grain diameter, as well as the contact stiffness. [Work supported by ONR, Ocean Acoustics.]