English necessity modals with priority meanings are (more or less) neatly divided into two groups by a battery of various tests: must and have to behave not like should and ought do. The usual conclusion drawn from this is that there exists a categorical distinction between strong-necessity and weak-necessity modals. I will show that there is in fact no such category. Using data from East Slavic, I will demonstrate that, first, necessity modals need not divide into two such neat classes, and second, that their behavior on the ``tests for weak necessity'' can actually be explained from more basic semantic properties that we need in the modal semantics anyway, such as the set of modal flavors a particular word may express. What makes English special is that several coincidences create the appearance of a single categorical distinction.