At very high frequencies, fundamental-frequency difference limens (F0DLs) for five-component harmonic complex tones can be better than predicted by optimal integration of information, assuming performance is limited by noise at the peripheral level, but are in line with predictions based on more central sources of noise. This study investigates whether there is a minimum number of harmonic components needed for such super-optimal integration effects and if harmonic range or inharmonicity affects this super-optimal integration. Results show super-optimal integration, even with two harmonic components and for most combinations of consecutive harmonic, but not inharmonic, components.