Redundant modification in referring expression production varies both within language (e.g., English speakers produce more redundant color than size modifiers) and cross-linguistically (e.g., English speakers produce more redundant color modifiers than Spanish speakers). It is an open question whether these asymmetries are the result of asymmetries in the general referential utility of color and size modifiers or of incremental language processing pressures. Cross-linguistic investigations of redundant modification are important to this debate: similar cross-linguistic rates of redundant modification would suggest a strong role for general referential utility. In contrast, lower prevalence of redundant modification in languages with post-nominal modification suggests a strong role for incrementality. Here, we test whether differences in redundant modifier use are systematic for a particularly interesting language: Central Taurus Sign Language. As a language in its infancy, CTSL has no established conventions, and therefore provides us with a unique opportunity to explore how redundancy emerges in the initial stages of language formation. We also ask whether redundant modification patterns replicate in Turkish and we compare our results to English. Using data from these three languages, we evaluate computational models of referring expression production that each make different assumptions regarding the source of asymmetries in the production of redundant modifiers. The data suggest a limited role for incrementality, and support accounts of redundancy that center the role of referential utility. However, this conclusion is limited by data concerns.