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Wavelength conversion using cross-gain modulation (XGM) in quantum-dot (QD) semiconductor optical amplifiers (SOAs) is investigated. Small-signal measurements reveal that the XGM bandwidth as well as the conversion efficiency strongly depends on the bias current. Thus, it is possible to tune the XGM by increasing the current from a low efficiency with a 10-GHz bandwidth to a very efficient one with bandwidths well exceeding 40 GHz. Two different saturation mechanisms are responsible for this pronounced influence of the bias current: 1) total carrier depletion that leads to a slow broadband cross-gain saturation and 2) spectral hole burning that causes spectrally narrow-band high-speed XGM. With increasing current, the saturation by depleting the carrier reservoir, which feeds the QDs, is minimized, and therefore, spectral hole burning becomes more dominant. Large-signal wavelength conversion experiments using 50 ps pulses indicate that efficient high-speed XGM is feasible for pump and probe signal detuning up to 10 nm. With increasing detuning, larger pulse broadening and a decreasing efficiency are observed, consistent with the small-signal results. The results on the QD SOAs are compared to conventional quantum-well devices.