A new approach has been developed to treat large-angle and small-angle binary collisions in plasmas when the test particles' distribution function fα is an even function about the test velocity vα. In the approach, the Boltzmann collision operator is derived to be suitable for the plasma considered as weakly coupled (Coulomb logarithm ln Λ≥10) or moderately coupled (2≤lnΛ≤10). The modified collision operator has a direct and practical connection to the Rosenbluth potentials. In addition, with mαmβ(such as electron-ion collision or Lorentz-gas model) and vαvβ, the reduced electron-ion collision operator differs from the original Fokker-Planck operator for Coulomb collisions by terms of order 1/lnΛ.