Improvements in speech-recognition performance resulting from the addition of low-frequency information to electric (or vocoded) signals have attracted considerable interest in recent years. An important question is whether these improvements reflect a form of constructive perceptual interaction—whereby acoustic cues enhance the perception of electric or vocoded signals—or whether they can be explained without assuming any interaction. To address this question, speech-recognition performance was measured in 24 normal-hearing listeners using lowpass-filtered, vocoded, and “combined” (lowpass + vocoded) words presented either in quiet or in a realistic background (cafeteria noise), for different signal-to-noise ratios, different lowpass-filter cutoff frequencies, and different numbers of vocoder bands. The results of these measures were then compared to the predictions of three models of cue combination, including a “probability-summation” model and two Gaussian signal detection theory (SDT) models—one (the “independent-noises” model) involving pre-combination noises, and the other (the “late-noise” model) involving post-combination noise. Consistent with previous findings, speech-recognition performance with combined stimulation was significantly higher than performance with vocoded or lowpass stimuli alone, and it was also higher than predicted by the probability-summation model. The two Gaussian-SDT models could account quantitatively for the data. Moreover, a Bayesian model-comparison procedure demonstrated that, given the data, these two models were far more likely than the probability-summation model. Since these models do not involve any constructive-interaction mechanism, this demonstrates that constructive interactions are not needed to explain the combined-stimulation benefits measured in this study. It will be important for future studies to investigate whether this conclusion generalizes to other test conditions, including real EAS, and to further test the assumptions of these different models of the combined-stimulation advantage.