The "combined-stimulation advantage" refers to an improvement in speech recognition when cochlear-implant or vocoded stimulation is supplemented by low-frequency acoustic information. Previous studies have been interpreted as evidence for "super-additive" or "synergistic" effects in the combination of low-frequency and electric or vocoded speech information by human listeners. However, this conclusion was based on predictions of performance obtained using a suboptimal high-threshold model of information combination. The present study shows that a different model, based on Gaussian signal detection theory, can predict surprisingly large combined-stimulation advantages, even when performance with either information source alone is close to chance, without involving any synergistic interaction. A reanalysis of published data using this model reveals that previous results, which have been interpreted as evidence for super-additive effects in perception of combined speech stimuli, are actually consistent with a more parsimonious explanation, according to which the combined-stimulation advantage reflects an optimal combination of two independent sources of information. The present results do not rule out the possible existence of synergistic effects in combined stimulation; however, they emphasize the possibility that the combined-stimulation advantages observed in some studies can be explained simply by non-interactive combination of two information sources.