In research on grammatical gender, assignment and agreement are the two central notions. Genders are defined as systems of agreement classes, and the assignment of nouns to genders is reflected in the agreement they consistently trigger on associated elements. Yet, gender assignment and gender agreement are often discussed quite separately. This paper investigates the possibility that gender agreement is not only an overt manifestation of gender assignment, but that properties of agreement systems can themselves constrain the assignment systems they express. The paper discusses typological and diachronic evidence for the fact that not every type of assignment system can be expressed in every type of agreement system.