Brownian dynamics simulations of bead-spring chains were used to study the relaxation of an initially stretched DNA molecule in slitlike confinement. Taking into account excluded volume effects but neglecting hydrodynamic interactions, the simulations are able to reproduce the two relaxation times in the linear force regime that our group has experimentally studied and recently reported. The relaxation dynamics of the transverse dimensions are extensively studied, and a theoretical model is developed to describe them. The interplay between the longitudinal and the transverse dynamics is investigated and used to corroborate a physical model previously proposed to describe polymer relaxation in a slit.