The effect of the collision efficiency of particles deposited onto a rough substrate and the evolution of the deposit profile were investigated using 2D on-lattice Monte Carlo simulations. The case of a diffusive long-range transport regime as representative of the colloidal deposition from the suspended phase was considered. The initial profile of the substrate was modeled as a sinusoidal wave. The decay of the initial profile in the course of deposition was monitored by a decrease in the Fourier amplitude A(w) corresponding to the wavelength of the initial roughness. The best "memory" of the deposit, i.e., the slowest decay of A(w), was found to correspond to intermediate values (similar to0.1) of the collision efficiency.