This paper documents an unexpected interaction between modal flavour and modal force in the domain of the German necessity modals muss (≈ ‘must’) and soll (≈ ‘be supposed to’) and their Konjunktiv II-inflected versions müsste and sollte. We argue for the following three proposals. First, muss and soll have largely disjoint modal flavours, in both the root and epistemic domains. The root modal flavours of muss are deontic, teleological, and a restricted bouletic use, while root soll is lexically bouletic, allowing deontic inferences; epistemic muss is inferential, while epistemic soll is reportative. Second, the addition of Konjunktiv II counterfactual morphology can create weak necessity modals, as expected on the cross-linguistic account of von Fintel and Iatridou (2008). However, an unanticipated effect on modal flavor occurs. When soll turns into its Konjunktiv II form sollte, it not only becomes a weak necessity modal, it also changes its modal flavours to those of muss. Sollte is thus semantically a weak necessity form of muss, not of soll. Third, the Konjunktiv II form of muss, namely müsste, also shows an unexpected quirk. We analyze this as the interference of polite Konjunktiv II, analyzed as free factive subjunctive (Csipak 2015), with the weak necessity reading. The paper also includes a comparison of the German modals with English have to, should and be supposed to.