Absolute densities of singlet delta oxygen (SDO) molecules were measured using infrared optical emission spectroscopy in the flowing effluents of two different atmospheric-pressure plasma jets (APPJs): a capacitively coupled radio-frequency-driven jet (rf-APPJ) and a lower frequency kilohertz-driven dielectric barrier discharge jet. The plasma jets were operated in helium, with small admixtures of molecular oxygen (O2 < 2%). High absolute SDO densities of up to 6.2 × 1015 cm-3 were measured at approximately 10 cm downstream. The rf-APPJ seems to be much more efficient in producing SDO. The influence of different parameters, such as gas flows and mixtures and power coupled to the plasmas, on the production of SDO by the two APPJs has been investigated. Despite the considerable differences between the two plasma jets (excitation frequency, electric field direction, inter-electrode distance, plasma propagation), similar dependencies on the oxygen admixture and on the dissipated power were found in both APPJs. However, opposite trends were observed for the gas flow dependence. The results presented in this paper show that the control of the external operating conditions of each APPJ enables the tailoring of the SDO composition of both plasma effluents. This provides scope to tune the plasma jets for desired applications, e.g., in biomedicine.