A previous observation, which indicated that the beta-relaxation intensity of o-terphenyl is sensitive to the thermal history, is substantiated by dielectric relaxation experiments. Unlike the beta-processes of other materials, only the quenched glassy state of o-terphenyl displays this secondary relaxation feature. The beta-intensity is observed to decay gradually upon annealing and disappears altogether in the equilibrium liquid state at T > T-g. We compare the case of o-terphenyl with the concomitant signatures of D-sorbitol, which represents the more typical case of a glass-former which exhibits the slow beta-process also in the liquid state including the alpha-beta-merging scenario. We also present data of this alpha-beta-merging for D-sorbitol confined to pores of 5 nm diameter, indicating that no longer-ranged correlations are involved in the secondary process.