Optimal values of $alpha$ characterizing the linear dispersion property in the modified Boussinesq equations are determined by minimizing the combined relative errors of the phase and group velocities. The value of $alpha$ is fixed in previous studies, whereas it is varying in the present study. The phase and group velocities are calculated by using variable $alpha$ and compared to those of the linear Stokes wave theory and previous studies. It is found that the present study produces the best match to the linear Stokes theory.