[en] In recent years, the authors have investigated methods to improve the effectiveness of modeling collisional processes in particle-in-cell codes. Through the use of generalized collision models, plasma dynamics can be followed both in the regime of nearly collisionless plasmas as well as in the hydrodynamic limit of collisional plasmas. They have developed a collision-field method to treat both the case of collisions between unlike plasma species (inter-species collisions), through the use of a deterministic, grid-based force, and between particles of the same species (intra-species collisions), through the use of a Langevin equation. While the approach used for inter-species collisions is noise-free in that the collision experienced by a particle does not require any random numbers, such random numbers are used for intra-species collisions. This gives rise to a stochastic cooling effect inherent in the Langevin approach. In this paper, the authors concentrate on intra-species collisions and describe how the accuracy of the model can be improved by appropriate corrections to velocity and spatial moments