Two aspects of the relation between cubic‐difference‐tone (CDT) generation and suppression were investigated in normal hearing listeners. First, the effects of narrow‐band noise and sinusoids on the two processes were examined using a forward‐masking paradigm. Within individual listeners, cubic difference bands (CDBs) behaved much like CDTs whereas the suppression effects produced by narrow‐band noise were substantially less than those produced by sinusoids. These results suggest that at least partially different processes underlie the two phenomena. Second, the role of suppression in the difference between forward‐ and simultaneous‐masking estimates of CDB amplitude was investigated. The data across listeners were highly variable but indicated a more complicated interpretation than that proposed by Shannon and Houtgast [J. Acoust. Soc. Am.68, 825–829 (1980)].