An improved treatment of the coupling between the lateral and reptative motions in the lateral motion model of polymer melt dynamics is presented. Approximate analytical formulas are also provided for the monomer and center of mass mean squared displacements and for the diffusion constant. Scalings are given for all predicted regions, and expressions are presented for the corresponding crossover times and chain lengths. Results from the full calculations and the analytical expressions are compared with published data from simulations and experimental systems. The theoretical predictions are in excellent agreement with the simulation and experimental data. The results also demonstrate that the approximation analytical formulas agree extremely well with the full calculations. Given the simplicity and accuracy of these analytical expressions, they should facilitate the implementation of the theory and its comparison to experimental data.