  A hypergroup is stringent if $a \boxplus b$ is a singleton whenever $a \neq
-b$. A hyperfield is stringent if the underlying additive hypergroup is. Every
doubly distributive skew hyperfield is stringent, but not vice versa. We
present a classification of stringent hypergroups, from which a classification
of doubly distributive skew hyperfields follows. It follows from our
classification that every such hyperfield is a quotient of a skew field.
