Recent comparative semantics suggests that sign language makes use of the same logical resources as spoken language, but has richer mechanisms of iconic enrichment. It is often thought that when speech is analyzed in tandem with iconic gestures, 'expressive parity' is regained between speech and sign. But this comparison between sign-with-iconicity and speech-with-gestures turns out to be complex because iconic enrichments often have a non-at-issue status, as attested by their interaction with logical operators. We argue that the status of iconic enrichments is constrained by two parameters: ±internal, ±separate_time_slot. If an enrichment is effected by the internal modification of an expression (+internal) -e.g. by lengthening the word loooong in English, or the sign GROW in ASL -it can have any semantic status and can in particular be atissue. If an enrichment is an external addition to an expression (-internal) -as is the case of co-speech gestures in English -it does not make an at-issue contribution, but it may have the status of a presupposition or of a supplement. If an enrichment has a separate time slot (+separate_time_slot), it may not be trivial (= presupposed), and must thus be at-issue or supplemental. The generalization is assessed on the basis of vocal iconicity in spoken language, iconic modulations in sign language, co-speech/co-sign as well as postspeech/post-sign gestures and facial expressions in spoken and sign language, and also gestures that fully replace words in spoken language. Our typology suggests that there are systematic expressive differences between sign-with-iconicity and speech-with-gestures, and also that the semantic status of iconic enrichments can in part be predicted by parameters pertaining to their form.