Rendaku is a morphophonological process in Japanese, in which the first consonant of the second element of compounds becomes voiced (e.g. /ao-sora/ → [ao-zora] ‘blue sky’). In a recent paper, Kim (2022) argues that the presence of two nasals—but not one nasal— in the second element reduces the probability of Rendaku application (e.g. /umi-kamome/ → [umi-kamome], *[umi-gamome] ‘seagull’). This claim has an important consequence for grammatical theories, as it would constitute a case in which the influences of two segments add up to block a phonological process, a pattern that is referred to as “super-additive counting cumulativity.” We have reexamined the empirical basis of this claim, and have found that there are only four relevant lexical items. Moreover, two of these items actually undergo Rendaku almost all the time, and there are thus only two items whose Rendaku is clearly blocked. The empirical basis of the theoretical claim based on Rendaku thus seems to be weak at best. With this, we move on to the main contribution of this paper, which is a new nonce-word experiment that aimed to resolve the conflicting results from the previous studies on this topic. The results of the current experiment show that the applicability of Rendaku is not reduced by the presence of two nasal consonants.