This study used a correlational approach to clarify the mechanisms involved in modulation coding. Amplitude-modulation (AM) and frequency-modulation (FM) detection thresholds (AMDTs and FMDTs, respectively) were assessed for 70 normal-hearing listeners. In order to increase between-listeners variability in peripheral coding, participants with a wide range of age (20–70 years) were included. AMDTs and FMDTs were measured at a 5-Hz rate, using a 500-Hz sinusoidal carrier. FMDTs were also measured in the presence of an interfering AM to discourage the use of temporal-envelope cues. The results showed that AMDTs were significantly correlated with FMDTs, but not with FMDTs measured with interfering AM. FMDTs with and without interfering AM were significantly correlated with each other. This pattern of correlation proved to be robust, providing additional evidence that for low carrier frequencies, (i) low-rate AM and FM detection is based on a common code using temporal-envelope cues and (ii) low-rate FM detection is based on an additional code using cues distinct from temporal-envelope. The analyses also showed that age was correlated with FMDTs only. However, no significant difference was found when comparing the various correlations with age. Hence, the effects of age on modulation sensitivity remain unclear.