Sign language phonological parameters are somewhat analogous to phonemes in spoken language. Unlike phonemes, however, there is little linguistic literature arguing that these parameters interact at the sublexical level. This situation raises the question of whether such interaction in spoken language phonology is an artifact of the modality or whether sign language phonology has not been approached in a way that allows one to recognize sublexical parameter interaction. We present three studies in favor of the latter alternative: a shape-drawing study with deaf signers from six countries, an online dictionary study of American Sign Language, and a study of selected lexical items across 34 sign languages. These studies show that, once iconicity is considered, handshape and movement parameters interact at the sublexical level. Thus, consideration of iconicity makes transparent similarities in grammar across both modalities, allowing us to maintain certain key findings of phonological theory as evidence of cognitive architecture.