The possibility of neutral-beam pumping in a tandem mirror thermal-barrier region is explored. To reduce the necessary neutral-beam pumping power, substituting low- for high-energy neutral beams is investigated. With the help of a two-step square well model and a variational expression for the trapping current, the competition between the trapping process and the drag effect for the deeply trapped particles is illustrated. This competition can lead to a stable equilibrium with reduced pumping power.