  We present a relativistic Shakhov-type generalization of the Anderson-Witting
relaxation time model for the Boltzmann collision integral to modify the ratio
of momentum diffusivity to thermal diffusivity. This is achieved by modifying
the path on which the single particle distribution function $f_{\bk}$
approaches local equilibrium $f_{0\bk}$ by constructing an intermediate
Shakhov-type distribution $f_{{\rm S} \bk}$ similar to the 14-moment
approximation of Israel and Stewart. We illustrate the effectiveness of this
model in case of the Bjorken expansion of an ideal gas of massive particles and
the damping of longitudinal waves through an ultrarelativistic ideal gas.
