We study the afterglow of a pulsed barrier discharge in helium with a small admixture of neon (10^‒2%), which creates a plasma with a low density of metastable particles. The early afterglow of this discharge is free of processes involving the participation of metastable particles and has a purely recombination nature. The characteristics of the afterglow are interpreted based on a model taking into account vibrational kinetics and dissociative recombination of He+2 molecular ions. Comparison of experimental data and model solutions for fluxes of collisional–radiative recombination of He^+ ions with electrons and dissociative recombination leads to the conclusion that the latter process is more likely to be a source of the formation of excited atoms.