Many non-native speakers of English find it hard to use modal auxiliaries correctly. As far as the so-called ‘weak’ root modals of necessity are concerned, (learner) grammars fail to provide clear guidelines about the use of these modals in specific usage contexts. While differences between should and ought to are minimized, be supposed to tends to be marginalized and its semantic profile remains vague. A study of 1200 corpus examples reveals the overlapping and distinctive usage contexts of these auxiliaries and allows us to derive the parameters that play a role in their usage: source, discourse context and strength. The article offers precise definitions of each parameter and provides a clear semantic profile for each auxiliary, thus paving the way towards more useful proficiency guidelines in (learner) grammars.