It is shown that a new cut-off at small scattering angle should be introduced for the case of constant relative velocity. A new cut-off on the velocity increment should be introduced for varying relative velocity because the collisions are effective only if the kinetic energy is greater than the Coulomb potential energy, and/or the interaction distance is shorter than the Debye length. It is found that the Coulomb logarithm should be reduced to half the value of conventional plasma kinetic theory. Consequently, Fokker-Planck coefficients are modified and applied to both weakly and moderately coupled plasmas. The relaxation times increase and the cross-field electrical resistivity, electron diffusion and ion thermal conductivity are reduced to half for Maxwellian scatters. The drifting beam of field particles in the tail of the Maxwellian distribution can further modify the Fokker-Planck coefficients, increase the relaxation times and reduce the cross-field transport coefficients.